FANDOM


A natural number (i.e. 1, 2, 3, 4, 5, 6, etc.) is called a prime number (or a prime) if it has exactly two positive divisors, 1 and the number itself. Natural numbers greater than 1 that are not prime are called composite.

The first 1X5 prime numbers (all the prime numbers less than 1000) are:

2, 3, 5, 7, E, 11, 15, 17, 1E, 25, 27, 31, 35, 37, 3E, 45, 4E, 51, 57, 5E, 61, 67, 6E, 75, 81, 85, 87, 8E, 91, 95, X7, XE, E5, E7, 105, 107, 111, 117, 11E, 125, 12E, 131, 13E, 141, 145, 147, 157, 167, 16E, 171, 175, 17E, 181, 18E, 195, 19E, 1X5, 1X7, 1E1, 1E5, 1E7, 205, 217, 21E, 221, 225, 237, 241, 24E, 251, 255, 25E, 267, 271, 277, 27E, 285, 291, 295, 2X1, 2XE, 2E1, 2EE, 301, 307, 30E, 315, 321, 325, 327, 32E, 33E, 347, 34E, 357, 35E, 365, 375, 377, 391, 397, 3X5, 3XE, 3E5, 3E7, 401, 40E, 415, 41E, 421, 427, 431, 435, 437, 447, 455, 457, 45E, 465, 46E, 471, 481, 485, 48E, 497, 4X5, 4E1, 4EE, 507, 511, 517, 51E, 527, 531, 535, 541, 545, 557, 565, 575, 577, 585, 587, 58E, 591, 59E, 5E1, 5E5, 5E7, 5EE, 611, 615, 617, 61E, 637, 63E, 647, 655, 661, 665, 66E, 675, 687, 68E, 695, 69E, 6X7, 6E1, 701, 705, 70E, 711, 71E, 721, 727, 735, 737, 745, 747, 751, 767, 76E, 771, 775, 77E, 785, 791, 797, 7X1, 7EE, 801, 80E, 817, 825, 82E, 835, 841, 851, 855, 85E, 865, 867, 871, 881, 88E, 8X5, 8X7, 8XE, 8E5, 8E7, 901, 905, 907, 90E, 91E, 921, 927, 955, 95E, 965, 971, 987, 995, 9X7, 9XE, 9E1, 9E5, 9EE, X07, X0E, X11, X17, X27, X35, X37, X3E, X41, X45, X4E, X5E, X6E, X77, X87, X91, X95, X9E, XX7, XXE, XE7, XEE, E11, E15, E1E, E21, E25, E2E, E31, E37, E45, E61, E67, E6E, E71, E91, E95, E97, EX5, EE5, EE7

The first 1000 prime numbers are listed below:

nnth primennth primennth primennth primennth primennth primennth primennth primennth primennth primennth primennth prime
12101591201110730118E7401253550131X16013X6770147778015487901619EX016E71E017877
2310259E202111530218EE402253750231EE6023X717024781802548E90261X7X026E75E02789E
351035E120311253031911403254550332056033X7E703479E80354X190361E7X036E77E0378E1
471045E5204112E3041915404254750432076043X9170447E180454X59046201X046E81E047905
5E1055E7205113530519214052555505320E6053X9570547E780554X79056207X056E9EE057907
6111065EE206114E3061931406255750632256063XE5706480580654E1906620EX066EX1E067917
71510761120711513071937407256550732276073XE77074815807550E9076227X077001E077921
81710861520811653081947408256E508322E6083E0E708481E8085515908622EX087005E087925
91E1096172091167309194E4092571509323E6093E11709482180955279096245X09700EE097941
X2510X61E20X118530X195540X257E50X324160X3E1E70X482580X553190X6247X0X7011E0X794E
E2710E63720E118E30E197140E258150E324760E3E2170E483180E553790E6257X0E7015E0E7955
103111063E2101197310197E410258E510324E6103E2E710483E81055459106261X10701EE10795E
113511164721111X13111981411259551132716113E477114845811554E9116265X11703EE117965
123711265521211X5312199541225X151232776123E4E712484E8125551912626EX127045E127971
133E11366121311X731319E7413260751332816133E51713486E813555E9136281X137051E13797E
144511466521411XE31419EE414261551432856143E55714488181455619146297X147055E14798E
154E11566E21511E73151X01415261751532916153E617154887815556591562X5X157057E1579X1
165111667521612013161X114162625516329E6163E75716488E816556791662E1X167085E1679XE
1757117687217120E3171X17417263151733076173E7E7174897817558591762EEX17708EE177X01
185E11868E21812113181X1E4182637518331E6183E8571848X781855879186327X187097E187X15
1961119695219121E3191X2E419264551933216193E877194901819558E9196331X1970XEE197X27
1X6711X69E21X123131X1X3541X265E51X332761X3E9771X490E81X559591X633EX1X70EEE1X7X35
1E6E11E6X721E123E31E1X4141E266551E332E61E3EXE71E491181E559E91E6345X1E7101E1E7X47
20751206E122012453201X45420267552033316203EE7720491E82055XE920634EX20710EE207X51
218112170122112553211X51421268552133356213EEE721492182155E59216351X217111E217X65
228512270522212573221X6E422268752233376224005722492582256079226357X22711EE227X6E
238712370E223125E3231X7142326X15233345623402E723492E8235615923636EX237125E237X77
248E12471122412613241X7542426X752433576244031724494782456259246375X247131E247X81
259112571E225126E3251X7742526XE5253361625403E7254951825562E9256377X257135E257X95
2695126721226127E3261X8742626E552633656264041726495582656379266387X267141E267XE1
27X712772722712813271XXE42726EE527337162740477274967827563E9276391X277151E277XEE
28XE12873522812953281XE14282715528337E628404E728496E828566E92863E5X28716EE287E01
29E512973722912973291XE74292717529338562940557294971829568192963E7X297175E297E07
2XE712X74522X12X132X1E0142X272552X33X162X405E72X497582X569192X6405X2X7187E2X7E0E
2E10512E74722E12X532E1E0742E273752E33X562E406772E498782E569792E6411X2E718EE2E7E11
3010713075123012X73301E0E430274153033X763040717304991830569E9306425X3071E1E307E15
3111113176723112E53311E15431274553133E1631407573149X183156X5931642EX3171E5E317E25
3211713276E23213013321E174322747532341763240857324X0183256X79326437X3271E7E327E27
3311E13377123313173331E27433274E533341E633408E7334X0E83356E79336441X337207E337E35
3412513477523413373341E2E434276E534342763440977344X158345701934644EX347215E347E37
3512E13577E235133E3351E3E4352771535343563540X77354X218355711935646EX357221E357E41
3613113678523613453361E414362781536343E63640XE7364X2E83657259366487X367225E367E5E
3713E13779123713513371E4E4372787537344563741017374X3183757279376495X377231E377E65
3814113879723813653381E51438279E538345163841117384X5783857359386497X387241E387E67
391451397X123913673391E6543927X75393457639411E7394X5E839574193964X5X397245E397E6E
3X14713X7EE23X136E33X1E6743X27E153X346763X413E73X4X6583X575E93X64X7X3X7257E3X7E85
3E15713E80123E137733E1E7E43E27E753E346E63E414573E4X6783E576193E64E7X3E7261E3E7E91
4016714080E240138E3401E854402811540347564041557404X77840577194064EEX407275E407E9E
4116E14181724113913411EX144128255413477641415E7414X7E84157779416505X41727EE417EX7
4217114282524213953421EE54422827542348164241617424X91842577E9426521X427287E428005
4317514382E24313X13432001443282E5433485643417E7434X9784357859436525X43728EE438007
4417E14483524413X734420054442835544348E64441877444E05844579E9446527X447295E448015
4518114584124513E134520074452837545349164541X17454E1584557X19456537X45729EE45802E
4618E14685124613E5346200E4462841546349E64641XE7464E2184657E19466551X4672X7E468041
4719514785524714053472011447284754734X164741E57474E2784757E7947655EX4772E1E478045
4819E14885E2481407348202E448285554834E564842077484E3584857EE9486561X4872EEE488047
491X514986524914253492037449285E54934EE649420E7494E37849580E949656EX49730EE49804E
4X1X714X86724X142E34X204744X286E54X351764X421174X4E3E84X581794X6571X4X7311E4X8065
4E1E114E87124E143134E205144E287E54E351E64E421774E4E5784E582194E6575X4E7317E4E8067
501E51508812501437350205E4502895550352E65042257504E6585058319506591X507321E50806E
511E715188E251143E35120614512897551354165142317514E71851583595165X5X517335E518075
522051528X52521445352206545228X1552356565242377524E85852583E9526607X527341E528081
532171538X72531457353206E45328X5553356E653423E7534E87853584E953660EX537347E53808E
5421E1548XE2541461354207145428EE554358765442457544E9585458559546617X547351E548091
552211558E5255146535520774552907555358E655426E7554EX785558579556621X557361E5580E7
562251568E725614673562085456292755635X565642817564EXE85658679566625X56736EE5680EE
5723715790125714713572087457292E55735E1657428E7574EE185758779576635X577371E578125
5824115890525814753582097458293155835E765842917585001858587E958663EX587377E588127
5924E159907259147E35920X5459293555935EE65942X1759500785958919596647X597391E598135
5X25115X90E25X148E35X20X745X293E55X360565X42XE75X501E85X589795X6657X5X7395E5X8137
5E25515E91E25E149535E20E545E294155E361765E42E175E502585E58XE95E6667X5E739EE5E8151
6025E160921260149E3602107460295156036216604305760503186058E59606671X6073X5E608155
6126716192726114E13612111461295556136276614307761503586158E79616675X6173XEE61816E
6227116295526214E53622115462296756236356624321762504186259059626681X6273EEE628175
6327716395E26314EE363211E46329915633637663434176350458635911963669EX637415E638187
6427E164965264150E3642127464299E56436456644357764504E864592796466X1X647421E648195
652851659712651517365213146529X5565365566543617655057865593196566E5X657427E658197
662911669872661521366213746629E5566366166643757665061866595E9666707X667435E66819E
672951679952671525367214E4672X07567366E667438E767506786759619676715X677441E6781E7
682X11689X72681547368215E4682X115683671668439576850778685985968671EX687457E688227
692XE1699XE269156136921614692X1E569367E669439776950818695987969672EX69745EE698231
6X2E116X9E126X156E36X216546X2X2E56X368766X43E176X508586X59X596X673EX6X7471E6X8235
6E2EE16E9E526E157736E217746E2X3156E369766E43E576E508E86E59XE96E6751X6E7477E6E823E
703011709EE270157E37021814702X3557036X567043EE770509587059E19706757X707491E708251
71307171X07271158537121854712X3E5713705671440177150X187159EE971675EX71749EE718255
7230E172X0E272158737221914722X475723707672440E77250E78725X0E9726777X7274X7E728271
73315173X112731591373219E4732X51573370E673441777350EE8735X11973677EX7374E5E73827E
74321174X1727415XE37421X74742X5E5743717674442577451178745X17974678EX747505E748291
75325175X2727515EE37521E14752X615753721675442E775511E8755X1E9756795X757507E7582XE
76327176X35276160137621E74762X6557637256764435776512E8765X279766797X767511E7682E5
7732E177X37277161537722154772X775773731677444177751318775X4597767X1X777521E7782E7
7833E178X3E2781621378221E4782X8157837476784445778513E8785X4E97867X7X787531E788321
79347179X41279162537922214792X875793755679444E77951458795X5197967EEX797561E798331
7X34E17XX4527X163537X222E47X2X8E57X375E67X445177X514787X5X5E97X6807X7X7565E7X833E
7E35717EX4E27E164737E224147E2X9557E376567E445E77E515587E5X6797E6825X7E756EE7E8355
8035E180X5E280165538022454802X975803767680446178051658805X6E9806827X807577E808357
81365181X6E2811657381224E4812XX55813771681447178151678815X75981684EX81757EE81835E
82375182X77282165E38222654822XX7582377E6824475782516E8825X819826857X827585E828371
83377183X87283166738322674832XEE583378E683447E78351878835X859836861X837587E838377
84391184X91284167138422754842E0E5843791684448578451918845X959846865X84758EE848395
85397185X95285167738522874852E17585379E685448778551E78855XXE9856881X8575X5E8583XE
863X5186X9E286167E386228E4862E3158637X5686449778652018865XEE9866885X8675E5E8683E1
873XE187XX7287168138722914872E3558737XE687449E78752058875E179876895X8775EEE878401
883E5188XXE2881685388229E4882E3E58837E568844E178852118885E1E98868E5X887607E888407
893E7189XE7289168E38922E14892E4E58938016894507789521E8895E259896911X897611E89840E
8X40118XXEE28X169738X22E548X2E5158X380768X450E78X522E88X5E2E98X6915X8X7617E8X8417
8E40E18EE1128E169E38E230148E2E5758E381568E451578E523588E5E3798E6921X8E761EE8E841E
90415190E1529016X139023174902E61590381E690453179052378905E3E990692EX907635E908427
9141E191E1E29116X7391231E4912E6759138216914535791525E8915E419916931X917637E918431
92421192E2129216E539223254922E8E5923827692454179252618925E559926945X92763EE92843E
93427193E2529316E739323274932E955933831693454779352678935E659936947X937641E938441
94431194E2E2941705394232E4942EX75943837694454E794526E8945E679946957X947661E948451
95435195E31295171139523354952EXE5953845695455779552718955E759956967X957665E958467
96437196E37296171539623374962EE75963851696455E79652858965E819966995X96766EE968475
97447197E452971727397234749730055973871697457179752958975E8E9976997X977675E978487
98455198E612981735398234E49830115983877698457779852978985E91998699EX987687E98849E
99457199E672991745399236749930215993895699457E79952X18995E9599969X5X9976E1E9984E1
9X45E19XE6E29X174739X238549X303759X389769X459179X52XE89X5E9E99X69E5X9X76E7E9X84E5
9E46519EE7129E175139E239549E303E59E38E169E45X179E52E789E5EE199E69EEX9E76EEE9E84EE
X046E1X0E912X017553X023974X030415X038E56X045X57X053178X060019X06X05XX07705EX08505
X14711X1E952X117573X1239E4X130455X139016X145X77X153278X1601E9X16X11XX17715EX18507
X24811X2E972X2176E3X223X54X230655X2390E6X246117X253318X260279X26X17XX2771EEX28511
X34851X3EX52X317813X323XE4X330755X339356X346157X353478X3604E9X36X1EXX37737EX38515
X448E1X4EE52X417853X423E14X4307E5X439416X446357X453518X460519X46X21XX4773EEX48517
X54971X5EE72X5178E3X523E74X530815X539576X5463E7X553558X560559X56X27XX57747EX5853E
X64X51X610052X617973X624154X630955X6395E6X646457X653678X660719X66X47XX6774EEX68541
X74E11X710112X717X13X724174X7309E5X739616X746557X753718X760759X76X4EXX77757EX78565
X84EE1X810172X817X53X824214X830X55X8396E6X846657X853758X860779X86X67XX87761EX8856E
X95071X910212X917EE3X924354X930E75X939756X946777X953858X9607E9X96X75XX97767EX98571
XX5111XX10272XX18073XX243E4XX31055XX39776XX46817XX53918XX60919XX6X7EXXX776EEXX8575
XE5171XE10412XE18153XE244E4XE31175XE39816XE46857XE53978XE609E9XE6X85XXE7795EXE857E
E051E1E010472E0181E3E024514E0311E5E039856E046877E053X78E060XE9E06X97XE07797EE08591
E15271E1104E2E118253E124574E131455E1399E6E1468E7E153XE8E160E19E16X9EXE177X5EE18595
E25311E210512E218313E224674E2314E5E239X76E246X57E253E58E261019E26XX5XE277E5EE285X5
E35351E310612E3183E3E3247E4E331555E339E76E346XE7E354058E361159E36XXEXE37801EE385E7
E45411E4106E2E4184E3E424814E4315E5E43X116E446EE7E4540E8E461179E46XE1XE4780EEE4860E
E55451E5107E2E518613E524854E531675E53X256E547077E5541E8E5613E9E56E01XE57817EE58621
E65571E610872E618653E6248E4E631715E63X2E6E647117E654218E661479E66E07XE67837EE68625
E75651E7109E2E7186E3E724X14E731755E73X316E747157E754358E761659E76E15XE77841EE7862E
E85751E810E12E818753E824X54E831775E83X416E847257E854518E861719E86E17XE87851EE88637
E95771E910E72E918773E924X74E931875E93X476E947277E954558E961759E96E25XE97855EE98641
EX5851EX10EE2EX189E3EX25014EX31915EX3X556EX47377EX54578EX617E9EX6E2EXEX7867EEX8645
EE5871EE11012EE18X13EE25214EE31955EE3X576EE47617EE54658EE61859EE6E47XEE786EEEE864E
10058E200110530018XE400252E50031976003X657004775800547E9006197X006E4EE00787510008655

Except 2 and 3, all primes end with 1, 5, 7 or E. The first k such that all of 10k, 10k + 1, 10k + 2, ..., 10k + E are composite is 38, i.e. all of 380, 381, 382, ..., 38E are composite. (numbers k such that all of 10k, 10k + 1, 10k + 2, ..., 10k + E are composite are 38, 5X, 60, 62, 89, 93, 94, E0, E5, E8, ...)

The maximal gaps of the primes less than 1000 is (927, 955), the gap (the difference of these two numbers) is 2X (i.e. there are 29 consecutive composites between 927 and 955).

The density of primes end with 1 is a relatively low (< 1/4), but the density of primes end with 5, 7 and E are nearly equal (all are a little more than 1/4). (i.e. for a given natural number N, the number of primes end with 1 less than N is usually smaller than the number of primes end with 5 (or 7, or E) less than N) e.g. For all 1426 primes < 10000, there are 3E8 primes (2E.3%) end with 1, 410 primes (30.3%) end with 5, 412 primes (30.5%) end with 7, 406 primes (2E.E%) end with E. It is conjectured that for every natural number N ≥ 10, the number of primes end with 1 less than N is smaller than the number of primes end with 5 (or 7, or E) less than N. (Note: the percentage in this section are also in dozenal, i.e. 20% means 0.2 or 20/100 = 1/6, 36% means 0.36 or 36/100 = 7/20, 58.7% means 0.587 or 587/1000)

13665 is the smallest prime p such that the number of primes end with 1 or 5 ≤ p is more than the number of primes end with 3, 7 or E ≤ p (i.e. congruent to 1 or 3 mod 4, see [1], of course, 3 is the only prime ends with 3). Besides, 9X03693X831 is the smallest prime p such that the number of primes end with 1 or 7 ≤ p is more than the number of primes end with 2, 5 or E ≤ p (i.e. congruent to 1 or 2 mod 3, see [2], of course, 2 is the only prime ends with 2). Besides, 2E69E is the smallest prime p such that the number of primes end with 1 or E ≤ p is more than the number of primes end with 5 or 7 ≤ p (of course, 2 is the only prime ends with 2, and 3 is the only prime ends with 3). Question: What is the smallest prime p such that the number of primes end with 1 ≤ p is more than the number of primes end with dp for at least one of d = 5, 7 or E?

"prime race" of last digit the smallest number which (the set which has "1") wins
{1, 5} v.s. {7, E} 5
{1, 7} v.s. {5, E} 9X03693X821
{1, E} v.s. {5, 7} 2E69E
{1, 5} v.s. {3, 7, E} 13665
{1, 7} v.s. {2, 5, E} 9X03693X831
{1, E} v.s. {2, 5, 7} 2EX51
{1} v.s. {5} ???
{1} v.s. {7} ???
{1} v.s. {E} ???

All squares of primes (except 2 and 3) end with 1.

There are 2X primes between 1 and 100, 23 primes between 101 and 200, 1X primes between 201 and 300, 1X primes between 301 and 400, 1E primes between 401 and 500, 1X primes between 501 and 600, 16 primes between 601 and 700, 1X primes between 701 and 800, 18 primes between 801 and 900, 16 primes between 901 and X00, 1X primes between X01 and E00, 17 primes between E01 and 1000.

There are about N/ln(N) primes less than N, where ln is the natural logarithm, i.e. the logarithm with base e = 2.875236069821... (see prime number theorem), thus there are about

$ \frac{10^n}{n \cdot ln(10)} $ primes less than 10n (i.e. with at most n digits), and ln(10) = 2.599E035E8169...

Ntotal numbers of primes less than Nnumbers of primes end with 1 less than Nnumbers of primes end with 5 less than Nnumbers of primes end with 7 less than Nnumbers of primes end with E less than N
101 50111
102 2X6998
103 1X551595958
104 14263E8410412406
105 1085231X432253225321X
106 X4E2027204272952730X27333
107 89X03E225430225675225609225747
108 779988E1XE4X791XE57331XE58381XE5661
109 690E6823183297491832X9891832E1801832E147
10X 60719X34716194E948161958X00161958070161955749
10E 5587E58533
1010 5005711X90E

In the following list, bold and red for prime numbers.


1 2 3 4 5 6 7 8 9 X E 10

11 12 13 14 15 16 17 18 19 1X 1E 20

21 22 23 24 25 26 27 28 29 2X 2E 30

31 32 33 34 35 36 37 38 39 3X 3E 40

41 42 43 44 45 46 47 48 49 4X 4E 50

51 52 53 54 55 56 57 58 59 5X 5E 60

61 62 63 64 65 66 67 68 69 6X 6E 70

71 72 73 74 75 76 77 78 79 7X 7E 80

81 82 83 84 85 86 87 88 89 8X 8E 90

91 92 93 94 95 96 97 98 99 9X 9E X0

X1 X2 X3 X4 X5 X6 X7 X8 X9 XX XE E0

E1 E2 E3 E4 E5 E6 E7 E8 E9 EX EE 100


101 102 103 104 105 106 107 108 109 10X 10E 110

111 112 113 114 115 116 117 118 119 11X 11E 120

121 122 123 124 125 126 127 128 129 12X 12E 130

131 132 133 134 135 136 137 138 139 13X 13E 140

141 142 143 144 145 146 147 148 149 14X 14E 150

151 152 153 154 155 156 157 158 159 15X 15E 160

161 162 163 164 165 166 167 168 169 16X 16E 170

171 172 173 174 175 176 177 178 179 17X 17E 180

181 182 183 184 185 186 187 188 189 18X 18E 190

191 192 193 194 195 196 197 198 199 19X 19E 1X0

1X1 1X2 1X3 1X4 1X5 1X6 1X7 1X8 1X9 1XX 1XE 1E0

1E1 1E2 1E3 1E4 1E5 1E6 1E7 1E8 1E9 1EX 1EE 200


201 202 203 204 205 206 207 208 209 20X 20E 210

211 212 213 214 215 216 217 218 219 21X 21E 220

221 222 223 224 225 226 227 228 229 22X 22E 230

231 232 233 234 235 236 237 238 239 23X 23E 240

241 242 243 244 245 246 247 248 249 24X 24E 250

251 252 253 254 255 256 257 258 259 25X 25E 260

261 262 263 264 265 266 267 268 269 26X 26E 270

271 272 273 274 275 276 277 278 279 27X 27E 280

281 282 283 284 285 286 287 288 289 28X 28E 290

291 292 293 294 295 296 297 298 299 29X 29E 2X0

2X1 2X2 2X3 2X4 2X5 2X6 2X7 2X8 2X9 2XX 2XE 2E0

2E1 2E2 2E3 2E4 2E5 2E6 2E7 2E8 2E9 2EX 2EE 300


301 302 303 304 305 306 307 308 309 30X 30E 310

311 312 313 314 315 316 317 318 319 31X 31E 320

321 322 323 324 325 326 327 328 329 32X 32E 330

331 332 333 334 335 336 337 338 339 33X 33E 340

341 342 343 344 345 346 347 348 349 34X 34E 350

351 352 353 354 355 356 357 358 359 35X 35E 360

361 362 363 364 365 366 367 368 369 36X 36E 370

371 372 373 374 375 376 377 378 379 37X 37E 380

381 382 383 384 385 386 387 388 389 38X 38E 390

391 392 393 394 395 396 397 398 399 39X 39E 3X0

3X1 3X2 3X3 3X4 3X5 3X6 3X7 3X8 3X9 3XX 3XE 3E0

3E1 3E2 3E3 3E4 3E5 3E6 3E7 3E8 3E9 3EX 3EE 400


401 402 403 404 405 406 407 408 409 40X 40E 410

411 412 413 414 415 416 417 418 419 41X 41E 420

421 422 423 424 425 426 427 428 429 42X 42E 430

431 432 433 434 435 436 437 438 439 43X 43E 440

441 442 443 444 445 446 447 448 449 44X 44E 450

451 452 453 454 455 456 457 458 459 45X 45E 460

461 462 463 464 465 466 467 468 469 46X 46E 470

471 472 473 474 475 476 477 478 479 47X 47E 480

481 482 483 484 485 486 487 488 489 48X 48E 490

491 492 493 494 495 496 497 498 499 49X 49E 4X0

4X1 4X2 4X3 4X4 4X5 4X6 4X7 4X8 4X9 4XX 4XE 4E0

4E1 4E2 4E3 4E4 4E5 4E6 4E7 4E8 4E9 4EX 4EE 500


501 502 503 504 505 506 507 508 509 50X 50E 510

511 512 513 514 515 516 517 518 519 51X 51E 520

521 522 523 524 525 526 527 528 529 52X 52E 530

531 532 533 534 535 536 537 538 539 53X 53E 540

541 542 543 544 545 546 547 548 549 54X 54E 550

551 552 553 554 555 556 557 558 559 55X 55E 560

561 562 563 564 565 566 567 568 569 56X 56E 570

571 572 573 574 575 576 577 578 579 57X 57E 580

581 582 583 584 585 586 587 588 589 58X 58E 590

591 592 593 594 595 596 597 598 599 59X 59E 5X0

5X1 5X2 5X3 5X4 5X5 5X6 5X7 5X8 5X9 5XX 5XE 5E0

5E1 5E2 5E3 5E4 5E5 5E6 5E7 5E8 5E9 5EX 5EE 600


601 602 603 604 605 606 607 608 609 60X 60E 610

611 612 613 614 615 616 617 618 619 61X 61E 620

621 622 623 624 625 626 627 628 629 62X 62E 630

631 632 633 634 635 636 637 638 639 63X 63E 640

641 642 643 644 645 646 647 648 649 64X 64E 650

651 652 653 654 655 656 657 658 659 65X 65E 660

661 662 663 664 665 666 667 668 669 66X 66E 670

671 672 673 674 675 676 677 678 679 67X 67E 680

681 682 683 684 685 686 687 688 689 68X 68E 690

691 692 693 694 695 696 697 698 699 69X 69E 6X0

6X1 6X2 6X3 6X4 6X5 6X6 6X7 6X8 6X9 6XX 6XE 6E0

6E1 6E2 6E3 6E4 6E5 6E6 6E7 6E8 6E9 6EX 6EE 700


701 702 703 704 705 706 707 708 709 70X 70E 710

711 712 713 714 715 716 717 718 719 71X 71E 720

721 722 723 724 725 726 727 728 729 72X 72E 730

731 732 733 734 735 736 737 738 739 73X 73E 740

741 742 743 744 745 746 747 748 749 74X 74E 750

751 752 753 754 755 756 757 758 759 75X 75E 760

761 762 763 764 765 766 767 768 769 76X 76E 770

771 772 773 774 775 776 777 778 779 77X 77E 780

781 782 783 784 785 786 787 788 789 78X 78E 790

791 792 793 794 795 796 797 798 799 79X 79E 7X0

7X1 7X2 7X3 7X4 7X5 7X6 7X7 7X8 7X9 7XX 7XE 7E0

7E1 7E2 7E3 7E4 7E5 7E6 7E7 7E8 7E9 7EX 7EE 800


801 802 803 804 805 806 807 808 809 80X 80E 810

811 812 813 814 815 816 817 818 819 81X 81E 820

821 822 823 824 825 826 827 828 829 82X 82E 830

831 832 833 834 835 836 837 838 839 83X 83E 840

841 842 843 844 845 846 847 848 849 84X 84E 850

851 852 853 854 855 856 857 858 859 85X 85E 860

861 862 863 864 865 866 867 868 869 86X 86E 870

871 872 873 874 875 876 877 878 879 87X 87E 880

881 882 883 884 885 886 887 888 889 88X 88E 890

891 892 893 894 895 896 897 898 899 89X 89E 8X0

8X1 8X2 8X3 8X4 8X5 8X6 8X7 8X8 8X9 8XX 8XE 8E0

8E1 8E2 8E3 8E4 8E5 8E6 8E7 8E8 8E9 8EX 8EE 900


901 902 903 904 905 906 907 908 909 90X 90E 910

911 912 913 914 915 916 917 918 919 91X 91E 920

921 922 923 924 925 926 927 928 929 92X 92E 930

931 932 933 934 935 936 937 938 939 93X 93E 940

941 942 943 944 945 946 947 948 949 94X 94E 950

951 952 953 954 955 956 957 958 959 95X 95E 960

961 962 963 964 965 966 967 968 969 96X 96E 970

971 972 973 974 975 976 977 978 979 97X 97E 980

981 982 983 984 985 986 987 988 989 98X 98E 990

991 992 993 994 995 996 997 998 999 99X 99E 9X0

9X1 9X2 9X3 9X4 9X5 9X6 9X7 9X8 9X9 9XX 9XE 9E0

9E1 9E2 9E3 9E4 9E5 9E6 9E7 9E8 9E9 9EX 9EE X00


X01 X02 X03 X04 X05 X06 X07 X08 X09 X0X X0E X10

X11 X12 X13 X14 X15 X16 X17 X18 X19 X1X X1E X20

X21 X22 X23 X24 X25 X26 X27 X28 X29 X2X X2E X30

X31 X32 X33 X34 X35 X36 X37 X38 X39 X3X X3E X40

X41 X42 X43 X44 X45 X46 X47 X48 X49 X4X X4E X50

X51 X52 X53 X54 X55 X56 X57 X58 X59 X5X X5E X60

X61 X62 X63 X64 X65 X66 X67 X68 X69 X6X X6E X70

X71 X72 X73 X74 X75 X76 X77 X78 X79 X7X X7E X80

X81 X82 X83 X84 X85 X86 X87 X88 X89 X8X X8E X90

X91 X92 X93 X94 X95 X96 X97 X98 X99 X9X X9E XX0

XX1 XX2 XX3 XX4 XX5 XX6 XX7 XX8 XX9 XXX XXE XE0

XE1 XE2 XE3 XE4 XE5 XE6 XE7 XE8 XE9 XEX XEE E00


E01 E02 E03 E04 E05 E06 E07 E08 E09 E0X E0E E10

E11 E12 E13 E14 E15 E16 E17 E18 E19 E1X E1E E20

E21 E22 E23 E24 E25 E26 E27 E28 E29 E2X E2E E30

E31 E32 E33 E34 E35 E36 E37 E38 E39 E3X E3E E40

E41 E42 E43 E44 E45 E46 E47 E48 E49 E4X E4E E50

E51 E52 E53 E54 E55 E56 E57 E58 E59 E5X E5E E60

E61 E62 E63 E64 E65 E66 E67 E68 E69 E6X E6E E70

E71 E72 E73 E74 E75 E76 E77 E78 E79 E7X E7E E80

E81 E82 E83 E84 E85 E86 E87 E88 E89 E8X E8E E90

E91 E92 E93 E94 E95 E96 E97 E98 E99 E9X E9E EX0

EX1 EX2 EX3 EX4 EX5 EX6 EX7 EX8 EX9 EXX EXE EE0

EE1 EE2 EE3 EE4 EE5 EE6 EE7 EE8 EE9 EEX EEE 1000


Numbers k such that all of 10k+1, 10k+5, 10k+7 and 10k+E are primes are

1, 3, 8, 32, 5E, 61, 90, 11X, 200, 274, 468, 607, 804, 936, E2X, ...

Numbers k such that none of 10k+1, 10k+5, 10k+7 and 10k+E are primes are

38, 5X, 60, 62, 89, 93, 94, E0, E5, E8, 103, 10X, 117, 122, 132, 141, 14X, 153, 155, 177, 185, 188, 190, 196, 19X, 1X9, 1E9, 220, 223, 225, 22X, 235, 237, 240, 249, 24E, 251, 25E, 269, 270, 275, 280, 288, 291, 297, 298, 2E2, 2E7, 305, 312, 313, 321, 325, 326, 32X, 32E, 339, 340, 350, 353, 355, 357, 359, 36E, 386, 388, 38X, 391, 392, 3X0, 3X8, 3XX, 3E3, 401, 40E, 412, 419, 425, 427, 431, 433, 43X, 44X, 452, 456, 458, 45E, 460, 462, 469, 474, 475, 47X, 485, 487, 48E, 493, 49E, 4X4, 4X8, 4XX, 4XE, 4E4, 510, 517, 51X, 524, 530, 544, 549, 557, 564, 565, 567, 588, 594, 597, 599, 5X3, 5E0, 5EX, 603, 606, 608, 612, 615, 621, 623, 627, 630, 631, 63X, 645, 647, 651, 654, 658, 65E, 674, 676, 681, 683, 687, 68X, 690, 697, 698, 6X3, 6X5, 6E3, 6E5, 6E6, 6EE, 702, 706, 707, 719, 71X, 738, 740, 746, 748, 754, 755, 759, 762, 765, 769, 76X, 772, 777, 778, 782, 788, 78X, 793, 799, 79E, 7XX, 7E7, 7EE, 803, 805, 80X, 810, 811, 814, 81X, 820, 821, 824, 826, 828, 830, 831, 834, 836, 838, 84X, 852, 855, 858, 861, 868, 876, 881, 882, 885, 88E, 897, 8X6, 8E6, 8EX, 903, 90E, 910, 911, 91E, 920, 922, 927, 932, 933, 935, 942, 943, 946, 949, 951, 954, 95X, 964, 967, 972, 980, 981, 985, 987, 990, 995, 998, 9X6, 9XE, 9E9, 9EE, X02, X07, X18, X1E, X25, X26, X2X, X38, X41, X47, X50, X52, X61, X78, X83, X86, X8E, X92, X94, X96, XX7, XX8, XXX, XE1, XE5, XE8, XEX, E04, E07, E08, E11, E13, E22, E24, E25, E29, E36, E40, E43, E44, E45, E47, E53, E58, E60, E62, E75, E82, E90, E96, E99, EX0, EX1, EX3, EXX, EXE, EE6, ...

In the following table, numbers shaded in black are units (0-almost primes), numbers shaded in cyan are primes (1-almost primes), numbers shaded in magenta are semiprimes (2-almost primes), numbers shaded in yellow are 3-almost primes, numbers shaded in blue are 4-almost primes, numbers shaded in green are 5-almost primes, and numbers shaded in red are 6-almost primes.

1 2 3 4 5 6 7 8 9 X E 10
11 12 13 14 15 16 17 18 19 1X 1E 20
21 22 23 24 25 26 27 28 29 2X 2E 30
31 32 33 34 35 36 37 38 39 3X 3E 40
41 42 43 44 45 46 47 48 49 4X 4E 50
51 52 53 54 55 56 57 58 59 5X 5E 60
61 62 63 64 65 66 67 68 69 6X 6E 70
71 72 73 74 75 76 77 78 79 7X 7E 80
81 82 83 84 85 86 87 88 89 8X 8E 90
91 92 93 94 95 96 97 98 99 9X 9E X0
X1 X2 X3 X4 X5 X6 X7 X8 X9 XX XE E0
E1 E2 E3 E4 E5 E6 E7 E8 E9 EX EE 100
101 102 103 104 105 106 107 108 109 10X 10E 110
111 112 113 114 115 116 117 118 119 11X 11E 120
121 122 123 124 125 126 127 128 129 12X 12E 130
131 132 133 134 135 136 137 138 139 13X 13E 140
141 142 143 144 145 146 147 148 149 14X 14E 150
151 152 153 154 155 156 157 158 159 15X 15E 160
161 162 163 164 165 166 167 168 169 16X 16E 170
171 172 173 174 175 176 177 178 179 17X 17E 180
181 182 183 184 185 186 187 188 189 18X 18E 190
191 192 193 194 195 196 197 198 199 19X 19E 1X0
1X1 1X2 1X3 1X4 1X5 1X6 1X7 1X8 1X9 1XX 1XE 1E0
1E1 1E2 1E3 1E4 1E5 1E6 1E7 1E8 1E9 1EX 1EE 200
201 202 203 204 205 206 207 208 209 20X 20E 210
211 212 213 214 215 216 217 218 219 21X 21E 220
221 222 223 224 225 226 227 228 229 22X 22E 230
231 232 233 234 235 236 237 238 239 23X 23E 240
241 242 243 244 245 246 247 248 249 24X 24E 250
251 252 253 254 255 256 257 258 259 25X 25E 260
261 262 263 264 265 266 267 268 269 26X 26E 270
271 272 273 274 275 276 277 278 279 27X 27E 280
281 282 283 284 285 286 287 288 289 28X 28E 290
291 292 293 294 295 296 297 298 299 29X 29E 2X0
2X1 2X2 2X3 2X4 2X5 2X6 2X7 2X8 2X9 2XX 2XE 2E0
2E1 2E2 2E3 2E4 2E5 2E6 2E7 2E8 2E9 2EX 2EE 300
301 302 303 304 305 306 307 308 309 30X 30E 310
311 312 313 314 315 316 317 318 319 31X 31E 320
321 322 323 324 325 326 327 328 329 32X 32E 330
331 332 333 334 335 336 337 338 339 33X 33E 340
341 342 343 344 345 346 347 348 349 34X 34E 350
351 352 353 354 355 356 357 358 359 35X 35E 360
361 362 363 364 365 366 367 368 369 36X 36E 370
371 372 373 374 375 376 377 378 379 37X 37E 380
381 382 383 384 385 386 387 388 389 38X 38E 390
391 392 393 394 395 396 397 398 399 39X 39E 3X0
3X1 3X2 3X3 3X4 3X5 3X6 3X7 3X8 3X9 3XX 3XE 3E0
3E1 3E2 3E3 3E4 3E5 3E6 3E7 3E8 3E9 3EX 3EE 400
401 402 403 404 405 406 407 408 409 40X 40E 410
411 412 413 414 415 416 417 418 419 41X 41E 420
421 422 423 424 425 426 427 428 429 42X 42E 430
431 432 433 434 435 436 437 438 439 43X 43E 440
441 442 443 444 445 446 447 448 449 44X 44E 450
451 452 453 454 455 456 457 458 459 45X 45E 460
461 462 463 464 465 466 467 468 469 46X 46E 470
471 472 473 474 475 476 477 478 479 47X 47E 480
481 482 483 484 485 486 487 488 489 48X 48E 490
491 492 493 494 495 496 497 498 499 49X 49E 4X0
4X1 4X2 4X3 4X4 4X5 4X6 4X7 4X8 4X9 4XX 4XE 4E0
4E1 4E2 4E3 4E4 4E5 4E6 4E7 4E8 4E9 4EX 4EE 500
501 502 503 504 505 506 507 508 509 50X 50E 510
511 512 513 514 515 516 517 518 519 51X 51E 520
521 522 523 524 525 526 527 528 529 52X 52E 530
531 532 533 534 535 536 537 538 539 53X 53E 540
541 542 543 544 545 546 547 548 549 54X 54E 550
551 552 553 554 555 556 557 558 559 55X 55E 560
561 562 563 564 565 566 567 568 569 56X 56E 570
571 572 573 574 575 576 577 578 579 57X 57E 580
581 582 583 584 585 586 587 588 589 58X 58E 590
591 592 593 594 595 596 597 598 599 59X 59E 5X0
5X1 5X2 5X3 5X4 5X5 5X6 5X7 5X8 5X9 5XX 5XE 5E0
5E1 5E2 5E3 5E4 5E5 5E6 5E7 5E8 5E9 5EX 5EE 600
601 602 603 604 605 606 607 608 609 60X 60E 610
611 612 613 614 615 616 617 618 619 61X 61E 620
621 622 623 624 625 626 627 628 629 62X 62E 630
631 632 633 634 635 636 637 638 639 63X 63E 640
641 642 643 644 645 646 647 648 649 64X 64E 650
651 652 653 654 655 656 657 658 659 65X 65E 660
661 662 663 664 665 666 667 668 669 66X 66E 670
671 672 673 674 675 676 677 678 679 67X 67E 680
681 682 683 684 685 686 687 688 689 68X 68E 690
691 692 693 694 695 696 697 698 699 69X 69E 6X0
6X1 6X2 6X3 6X4 6X5 6X6 6X7 6X8 6X9 6XX 6XE 6E0
6E1 6E2 6E3 6E4 6E5 6E6 6E7 6E8 6E9 6EX 6EE 700
701 702 703 704 705 706 707 708 709 70X 70E 710
711 712 713 714 715 716 717 718 719 71X 71E 720
721 722 723 724 725 726 727 728 729 72X 72E 730
731 732 733 734 735 736 737 738 739 73X 73E 740
741 742 743 744 745 746 747 748 749 74X 74E 750
751 752 753 754 755 756 757 758 759 75X 75E 760
761 762 763 764 765 766 767 768 769 76X 76E 770
771 772 773 774 775 776 777 778 779 77X 77E 780
781 782 783 784 785 786 787 788 789 78X 78E 790
791 792 793 794 795 796 797 798 799 79X 79E 7X0
7X1 7X2 7X3 7X4 7X5 7X6 7X7 7X8 7X9 7XX 7XE 7E0
7E1 7E2 7E3 7E4 7E5 7E6 7E7 7E8 7E9 7EX 7EE 800
801 802 803 804 805 806 807 808 809 80X 80E 810
811 812 813 814 815 816 817 818 819 81X 81E 820
821 822 823 824 825 826 827 828 829 82X 82E 830
831 832 833 834 835 836 837 838 839 83X 83E 840
841 842 843 844 845 846 847 848 849 84X 84E 850
851 852 853 854 855 856 857 858 859 85X 85E 860
861 862 863 864 865 866 867 868 869 86X 86E 870
871 872 873 874 875 876 877 878 879 87X 87E 880
881 882 883 884 885 886 887 888 889 88X 88E 890
891 892 893 894 895 896 897 898 899 89X 89E 8X0
8X1 8X2 8X3 8X4 8X5 8X6 8X7 8X8 8X9 8XX 8XE 8E0
8E1 8E2 8E3 8E4 8E5 8E6 8E7 8E8 8E9 8EX 8EE 900
901 902 903 904 905 906 907 908 909 90X 90E 910
911 912 913 914 915 916 917 918 919 91X 91E 920
921 922 923 924 925 926 927 928 929 92X 92E 930
931 932 933 934 935 936 937 938 939 93X 93E 940
941 942 943 944 945 946 947 948 949 94X 94E 950
951 952 953 954 955 956 957 958 959 95X 95E 960
961 962 963 964 965 966 967 968 969 96X 96E 970
971 972 973 974 975 976 977 978 979 97X 97E 980
981 982 983 984 985 986 987 988 989 98X 98E 990
991 992 993 994 995 996 997 998 999 99X 99E 9X0
9X1 9X2 9X3 9X4 9X5 9X6 9X7 9X8 9X9 9XX 9XE 9E0
9E1 9E2 9E3 9E4 9E5 9E6 9E7 9E8 9E9 9EX 9EE X00
X01 X02 X03 X04 X05 X06 X07 X08 X09 X0X X0E X10
X11 X12 X13 X14 X15 X16 X17 X18 X19 X1X X1E X20
X21 X22 X23 X24 X25 X26 X27 X28 X29 X2X X2E X30
X31 X32 X33 X34 X35 X36 X37 X38 X39 X3X X3E X40
X41 X42 X43 X44 X45 X46 X47 X48 X49 X4X X4E X50
X51 X52 X53 X54 X55 X56 X57 X58 X59 X5X X5E X60
X61 X62 X63 X64 X65 X66 X67 X68 X69 X6X X6E X70
X71 X72 X73 X74 X75 X76 X77 X78 X79 X7X X7E X80
X81 X82 X83 X84 X85 X86 X87 X88 X89 X8X X8E X90
X91 X92 X93 X94 X95 X96 X97 X98 X99 X9X X9E XX0
XX1 XX2 XX3 XX4 XX5 XX6 XX7 XX8 XX9 XXX XXE XE0
XE1 XE2 XE3 XE4 XE5 XE6 XE7 XE8 XE9 XEX XEE E00
E01 E02 E03 E04 E05 E06 E07 E08 E09 E0X E0E E10
E11 E12 E13 E14 E15 E16 E17 E18 E19 E1X E1E E20
E21 E22 E23 E24 E25 E26 E27 E28 E29 E2X E2E E30
E31 E32 E33 E34 E35 E36 E37 E38 E39 E3X E3E E40
E41 E42 E43 E44 E45 E46 E47 E48 E49 E4X E4E E50
E51 E52 E53 E54 E55 E56 E57 E58 E59 E5X E5E E60
E61 E62 E63 E64 E65 E66 E67 E68 E69 E6X E6E E70
E71 E72 E73 E74 E75 E76 E77 E78 E79 E7X E7E E80
E81 E82 E83 E84 E85 E86 E87 E88 E89 E8X E8E E90
E91 E92 E93 E94 E95 E96 E97 E98 E99 E9X E9E EX0
EX1 EX2 EX3 EX4 EX5 EX6 EX7 EX8 EX9 EXX EXE EE0
EE1 EE2 EE3 EE4 EE5 EE6 EE7 EE8 EE9 EEX EEE 1000

The twin prime pairs below 100 are (3, 5), (5, 7), (E, 11), (15, 17), (25, 27), (35, 37), (4E, 51), (5E, 61), (85, 87), (8E, 91), (E5, E7), and there are only 47 twin prime pairs below 1000. Except (3, 5), all twin prime pairs end with (5, 7) or (E, 1), and it is conjectured that the density of them are the same.

Primes sorted by the last digit Edit

Gaussian primes are primes in the ring

$ Z[i]=Z[\zeta_4] $ , Eisenstein primes are primes in the ring

$ Z[\omega]=Z[\zeta_3]=Z[-\frac{1}{2}+\frac{\sqrt{3}}{2}i] $ .

  • The primes end with 1 are neither Gaussian primes nor Eisenstein primes.
  • The primes end with 5 (also the prime 2) are Eisenstein primes, but not Gaussian primes.
  • The primes end with 7 (also the prime 3) are Gaussian primes, but not Eisenstein primes.
  • The primes end with E are both Gaussian primes and Eisenstein primes.

The primes end with 1, 5, 7 and E are called 1-primes, 5-primes, 7-primes and E-primes, respectively.

1-primes: 11, 31, 51, 61, 81, 91, 111, 131, 141, 171, 181, 1E1, 221, 241, 251, 271, 291, 2X1, 2E1, 301, 321, 391, 401, 421, 431, 471, 481, 4E1, 511, 531, 541, 591, 5E1, 611, 661, 6E1, 701, 711, 721, 751, 771, 791, 7X1, 801, 841, 851, 871, 881, 901, 921, 971, 9E1, X11, X41, X91, E11, E21, E31, E61, E71, E91, 1011, 1021, 1041, 1051, 1061, 10E1, 1101, 1151, 11X1, 1201, 1211, 1231, 1261, 1281, 12X1, 1301, 1351, 1391, 13X1, 13E1, 1431, 1461, 1471, 14E1, 1521, 1561, 1591, 1601, 1621, 1671, 1681, 16X1, 1711, 1751, 1781, 17X1, 1831, 1861, 18X1, 1911, 1921, 1931, 1971, 1981, 1X01, 1X11, 1X41, 1X51, 1X71, 1XE1, 1E01, 1E41, 1E51, 1EX1, 2001, 2011, 2051, 2061, 2071, 2111, 2131, 2161, 2181, 2191, 21E1, 2221, 2241, 2291, 22E1, 2301, 23E1, 2421, 2451, 2481, 24X1, 2501, 2521, 2571, 2581, 25X1, 2631, 26X1, 2741, 2771, 2781, 27E1, 2811, 2841, 28X1, 2931, 2941, 2951, 2991, 2X11, 2X31, 2X51, 2X61, 2X81, 2E31, 2E51, 2E61, 3011, 3021, 3041, 3081, 3171, 3191, 31X1, 3241, 3271, 3281, 3291, 3321, 3331, 3361, 3371, 33X1, 33E1, 3451, 3481, 3491, 34X1, 3541, 35E1, 3621, 3661, 3671, 3721, 3731, 3771, 3791, 3801, 3821, 3831, 3851, 3871, 38E1, 3901, 3941, 3961, 3981, 3X11, 3X31, 3X41, 3X71, 3X91, 3E11, 3E21, 3E51, 3E61, 4031, 4041, 4071, 4101, 4111, 4161, 41X1, 4211, 4231, 4281, 4291, 42X1, 42E1, 4321, 4341, 4361, 43E1, 4401, 4441, 4451, 4461, 4471, 44E1, 4531, 4541, 4571, 4591, 45X1, 4611, 4681, 4711, 4761, 4781, 47E1, 4821, 4831, 4881, 4901, 4911, 4921, 4951, 4971, 4991, 49X1, 4X01, 4X21, 4X31, 4X91, 4E21, 4E71, 4EE1, 5001, 5031, 5041, 5061, 5081, 50X1, 5131, 5191, 5201, 5211, 5261, 5271, 52X1, 5331, 5351, 5371, 5391, 5421, 5451, 54X1, 54E1, 5531, 5551, 5561, 5681, 5691, 5701, 5711, 5741, 5761, 5771, 57X1, 57E1, 5821, 5831, 5891, 5911, 5931, 5961, 59E1, 5X11, 5X51, 5X81, 5E41, 5E81, 5E91, 5EE1, 6001, 6051, 6071, 6091, 60E1, 6101, 6171, 6201, 6261, 6281, 62E1, 6331, 6351, 6391, 6411, 6441, 6521, 6551, 6561, 6571, 6591, 6621, 6671, 6681, 66X1, 6751, 67X1, 6861, 6881, 6911, 6921, 6931, 6X11, 6X21, 6XE1, 6E01, 6E71, 6E81, 6EX1, 7001, 7011, 7051, 7101, 7111, 7131, 7141, 7151, 71E1, 7221, 7231, 7241, 7261, 72E1, 7311, 7321, 7341, 7351, 7361, 7371, 7391, 7421, 7441, 7471, 7491, 7511, 7521, 7531, 7561, 7611, 7641, 7661, 76E1, 7761, 7801, 7841, 7851, 78E1, 7921, 7941, 7971, 79X1, 7X01, 7X51, 7X81, 7XE1, 7E01, 7E11, 7E41, 7E91, 8041, 8081, 8091, 8151, 8231, 8251, 8271, 8291, 8321, 8331, 8371, 83E1, 8401, 8431, 8441, 8451, 84E1, 8511, 8541, 8571, 8591, 8621, 8641, 8691, 86E1, 8731, 8781, 8831, 8871, 8881, 8901, 8961, 8981, 89X1, 8X11, 8X21, 8X41, 8X71, 8X81, 8X91, 8E71, 8EE1, 9041, 9081, 9091, 9131, 91X1, 9231, 9241, 9251, 9261, 9281, 92E1, 9341, 9361, 9371, 9411, 9451, 94X1, 9501, 9551, 9581, 9591, 9601, 9631, 9651, 9701, 9711, 9761, 9781, 97E1, 9821, 9831, 9961, 99E1, 9X01, 9X31, 9X41, 9X51, 9X71, 9E01, 9E61, 9EX1, X011, X031, X051, X081, X091, X0X1, X121, X161, X171, X201, X211, X301, X321, X331, X341, X421, X461, X4X1, X4E1, X511, X541, X551, X581, X5X1, X5E1, X621, X631, X661, X671, X691, X701, X711, X721, X791, X801, X821, X841, X851, X871, X891, X8X1, X951, X971, XX31, XX61, XE41, XE91, E001, E051, E061, E0E1, E151, E171, E181, E1X1, E211, E231, E271, E2X1, E2E1, E301, E331, E341, E351, E411, E421, E481, E4E1, E521, E541, E561, E571, E5E1, E6X1, E711, E761, E771, E781, E7E1, E801, E811, E861, E891, E931, E941, E971, EX51, EX61, EX71, EE01, EE41, ...

5-primes: 5, 15, 25, 35, 45, 75, 85, 95, E5, 105, 125, 145, 175, 195, 1X5, 1E5, 205, 225, 255, 285, 295, 315, 325, 365, 375, 3X5, 3E5, 415, 435, 455, 465, 485, 4X5, 535, 545, 565, 575, 585, 5E5, 615, 655, 665, 675, 695, 705, 735, 745, 775, 785, 825, 835, 855, 865, 8X5, 8E5, 905, 955, 965, 995, 9E5, X35, X45, X95, E15, E25, E45, E95, EX5, EE5, 1005, 1105, 1115, 1125, 1135, 1165, 1185, 11X5, 1245, 1255, 1295, 12X5, 12E5, 1345, 1365, 1395, 13E5, 1405, 1425, 1445, 1465, 1475, 1495, 14E5, 1525, 1585, 1615, 1625, 1635, 1655, 1685, 16E5, 1705, 1715, 1735, 1745, 1755, 1785, 17X5, 1815, 1825, 1865, 1875, 1915, 1955, 1995, 1X35, 1X45, 1X75, 1E15, 1E65, 1E85, 1EE5, 2005, 2065, 2085, 20X5, 20E5, 2115, 2165, 2185, 2215, 2245, 2265, 2275, 22E5, 2325, 2335, 2385, 2395, 23X5, 2415, 2435, 2485, 24X5, 2535, 2545, 2555, 2565, 2595, 2615, 2625, 2645, 2665, 2675, 2685, 26E5, 2715, 2725, 2745, 2825, 2835, 2855, 2895, 28X5, 2935, 2955, 29X5, 29E5, 2X35, 2X65, 2X95, 2XX5, 2E35, 2E95, 3005, 3045, 3065, 3075, 3095, 30X5, 3105, 3145, 3155, 3175, 3195, 3205, 3225, 3285, 3335, 3345, 3365, 3385, 33X5, 3435, 3445, 3475, 3485, 34E5, 3565, 35X5, 3605, 3635, 3645, 3655, 36X5, 3705, 3725, 3755, 3765, 37X5, 37E5, 3815, 3845, 3895, 38E5, 3935, 3975, 3985, 3X25, 3X55, 3X65, 3X95, 3XE5, 3E55, 3E75, 3E85, 4005, 4055, 4075, 4085, 4145, 4155, 41E5, 4225, 4245, 4305, 4375, 4395, 43E5, 4425, 4435, 4445, 4475, 4485, 4515, 4535, 45X5, 4615, 4635, 4645, 4655, 4665, 4685, 46X5, 4715, 4725, 4775, 4805, 4815, 4825, 4845, 4925, 4955, 4975, 4X15, 4X65, 4E05, 4E15, 4E35, 4E65, 4E85, 4E95, 5025, 5035, 5045, 5085, 5095, 5145, 5155, 5165, 5205, 5235, 5285, 5295, 5355, 5375, 5385, 53E5, 5405, 5435, 5455, 5465, 54X5, 5515, 5545, 5565, 5585, 5595, 55E5, 5615, 5625, 56X5, 5725, 5735, 5785, 5835, 5855, 58E5, 5905, 5985, 59X5, 5X45, 5X75, 5X85, 5X95, 5E25, 5E55, 5E65, 5E75, 5E95, 6055, 6075, 6115, 6165, 6175, 6185, 6245, 6265, 62X5, 6345, 6375, 63E5, 6405, 6425, 6495, 64X5, 6505, 6525, 6575, 65X5, 6625, 6635, 6675, 66E5, 6715, 6795, 6825, 6865, 6885, 6895, 68E5, 6915, 6945, 6995, 69X5, 69E5, 6X05, 6X75, 6X85, 6XX5, 6E15, 6E25, 6E75, 7005, 7015, 7045, 7055, 7085, 7125, 7135, 7175, 71E5, 7215, 7225, 7245, 7275, 7295, 7335, 7395, 73X5, 7415, 7435, 74E5, 7505, 7565, 7585, 75X5, 75E5, 7635, 7665, 7675, 7705, 7715, 7795, 77X5, 77E5, 7855, 7875, 7905, 7925, 7955, 7965, 7X15, 7X35, 7X65, 7X95, 7E15, 7E25, 7E35, 7E65, 7E85, 8005, 8015, 8045, 8065, 8075, 8125, 8135, 8155, 8175, 8195, 8235, 8255, 82E5, 8355, 8395, 8475, 84E5, 8505, 8515, 8565, 8575, 8595, 85X5, 8625, 8645, 8655, 86X5, 8755, 87X5, 87E5, 8835, 8865, 8885, 88X5, 8915, 8925, 8935, 8945, 8995, 8X05, 8X55, 8X95, 8XE5, 8E05, 8E45, 8E55, 8E75, 9015, 9025, 9065, 9075, 9135, 9145, 9155, 9165, 9185, 9195, 9235, 9315, 9365, 9375, 9395, 9455, 9475, 9485, 94X5, 9525, 9565, 9575, 9605, 9615, 9655, 9665, 9695, 96E5, 9775, 9785, 9795, 98X5, 9935, 9945, 9975, 9X25, 9X35, 9X85, 9XX5, 9E45, X035, X045, X095, X0E5, X145, X155, X205, X225, X235, X275, X285, X295, X315, X365, X3X5, X445, X455, X485, X4X5, X535, X565, X575, X605, X675, X695, X6X5, X735, X745, X755, X795, X7X5, X825, X875, X915, X935, X9X5, X9E5, XX25, XX45, XX65, XE05, XE45, XEE5, E005, E025, E055, E095, E105, E125, E1E5, E205, E265, E2X5, E2E5, E315, E325, E385, E395, E3E5, E465, E495, E4X5, E555, E595, E5X5, E615, E635, E655, E665, E675, E685, E6X5, E705, E785, E795, E815, E835, E875, E885, E8E5, E925, E945, E955, E975, E9E5, EX25, EX85, EE75, EE85, EEX5, ...

7-primes: 7, 17, 27, 37, 57, 67, 87, X7, E7, 107, 117, 147, 157, 167, 1X7, 1E7, 217, 237, 267, 277, 307, 327, 347, 357, 377, 397, 3E7, 427, 437, 447, 457, 497, 507, 517, 527, 557, 577, 587, 5E7, 617, 637, 647, 687, 6X7, 727, 737, 747, 767, 797, 817, 867, 8X7, 8E7, 907, 927, 987, 9X7, X07, X17, X27, X37, X77, X87, XX7, XE7, E37, E67, E97, EE7, 1017, 1027, 1047, 1087, 10E7, 1107, 1167, 1197, 11X7, 11E7, 1257, 1297, 12X7, 1317, 1337, 1367, 1377, 13X7, 1407, 1437, 1457, 1467, 1517, 1547, 1577, 1587, 1647, 1657, 1667, 1677, 1697, 16X7, 16E7, 1727, 1747, 1757, 1797, 1807, 1877, 18E7, 1937, 1947, 19E7, 1X17, 1X77, 1X87, 1XE7, 1E07, 1E17, 1E27, 1E67, 2007, 2037, 2047, 2077, 2087, 2097, 20X7, 2107, 2127, 2137, 2177, 21X7, 21E7, 2267, 2287, 2317, 2327, 2337, 2347, 2367, 2397, 23E7, 2417, 2457, 2467, 24X7, 2537, 2547, 2557, 2607, 2617, 2637, 2687, 26X7, 2717, 2737, 2747, 2787, 27X7, 27E7, 2827, 2837, 2847, 2897, 2907, 2927, 2967, 2X07, 2X47, 2X77, 2X87, 2X97, 2XX7, 2E17, 2E57, 2E67, 2EX7, 2EE7, 3037, 30E7, 3117, 3167, 3177, 3187, 3197, 3207, 3227, 3247, 3277, 3307, 3327, 3337, 3357, 33X7, 3417, 3427, 3457, 3467, 3477, 3517, 3587, 35E7, 3617, 3627, 3637, 3687, 3697, 3707, 3717, 3747, 3767, 3807, 3827, 3837, 3877, 3897, 3957, 3977, 39X7, 39E7, 3X47, 3X57, 3X67, 3XE7, 3E47, 3E87, 3E97, 3EE7, 4047, 4067, 4097, 40X7, 4187, 4207, 4217, 4237, 4307, 4357, 4397, 4417, 4487, 4497, 4507, 4547, 4557, 4577, 45X7, 4677, 4687, 4707, 4727, 4737, 4777, 47E7, 4887, 4897, 48X7, 4947, 4967, 4987, 4X57, 4X67, 4X77, 4X97, 4E27, 4E37, 4E57, 4E87, 4EX7, 5007, 5057, 5067, 5077, 50E7, 5117, 5147, 5167, 5187, 51E7, 5237, 5267, 5297, 52E7, 5317, 5327, 5347, 5367, 5397, 53X7, 5457, 5487, 54X7, 5527, 5537, 5567, 5587, 5607, 5637, 5697, 56X7, 56E7, 5727, 5777, 57E7, 5817, 5857, 5867, 5877, 5897, 58E7, 5927, 5987, 5X17, 5X27, 5X67, 5E17, 5E37, 5E67, 6027, 6077, 6117, 6147, 6197, 61X7, 61E7, 6207, 6227, 6247, 6257, 6297, 6327, 6357, 6377, 6387, 63E7, 6437, 6487, 6497, 64X7, 64E7, 6527, 6537, 6607, 6617, 6647, 6657, 6667, 6707, 6757, 6777, 6797, 67X7, 6807, 6827, 6857, 6947, 6957, 6967, 6997, 6X17, 6X27, 6X47, 6X67, 6X97, 6E07, 6E17, 6E47, 6E77, 7057, 7097, 7187, 71E7, 7207, 7257, 7287, 72X7, 7317, 7347, 7377, 7427, 7457, 7477, 74X7, 7507, 7577, 7587, 7607, 7617, 7637, 7687, 76E7, 7737, 7747, 7757, 7767, 7797, 7817, 7837, 7867, 7877, 7907, 7917, 7X27, 7X47, 7X77, 7E07, 7E27, 7E37, 7E67, 7EX7, 8007, 8047, 8067, 80E7, 8127, 8137, 8187, 8197, 81E7, 8227, 82E7, 8357, 8377, 8407, 8417, 8427, 8467, 8487, 8507, 8517, 85E7, 8637, 8667, 8677, 86E7, 8717, 8747, 8777, 8797, 8807, 8847, 8897, 8917, 8957, 8967, 89E7, 8X07, 8X37, 8X47, 8X57, 8XX7, 8E17, 8E27, 8E37, 8E87, 9007, 9027, 9047, 9057, 9077, 9097, 90X7, 9127, 9137, 9177, 91X7, 9217, 9257, 9267, 9307, 9367, 9387, 93X7, 9447, 9487, 94E7, 9557, 9577, 95E7, 9627, 9687, 9707, 9737, 9777, 97E7, 9837, 9847, 98X7, 98E7, 9927, 9947, 9967, 9997, 99E7, 9X17, 9X47, 9X97, 9E27, 9E47, 9E57, 9E87, X017, X067, X087, X0E7, X107, X117, X137, X157, X197, X1X7, X227, X247, X277, X297, X2E7, X367, X397, X3X7, X3E7, X407, X447, X457, X487, X497, X537, X5X7, X647, X657, X667, X717, X767, X777, X7E7, X807, X817, X877, X907, X987, X997, XX57, XXE7, XE47, XE97, E037, E067, E127, E147, E157, E167, E197, E277, E2X7, E307, E327, E337, E357, E377, E387, E417, E487, E497, E527, E577, E597, E5E7, E617, E647, E677, E6E7, E707, E727, E747, E777, E7X7, E8X7, E917, E937, E947, E987, E9X7, E9E7, EX27, EX87, EX97, EE07, EE17, EE97, EEX7, EEE7, ...

E-primes: E, 1E, 3E, 4E, 5E, 6E, 8E, XE, 11E, 12E, 13E, 16E, 17E, 18E, 19E, 21E, 24E, 25E, 27E, 2XE, 2EE, 30E, 32E, 33E, 34E, 35E, 3XE, 40E, 41E, 45E, 46E, 48E, 4EE, 51E, 58E, 59E, 5EE, 61E, 63E, 66E, 68E, 69E, 70E, 71E, 76E, 77E, 7EE, 80E, 82E, 85E, 88E, 8XE, 90E, 91E, 95E, 9XE, 9EE, X0E, X3E, X4E, X5E, X6E, X9E, XXE, XEE, E1E, E2E, E6E, 104E, 106E, 107E, 109E, 10EE, 112E, 114E, 118E, 11XE, 120E, 121E, 123E, 125E, 126E, 127E, 133E, 136E, 138E, 142E, 143E, 147E, 148E, 149E, 14EE, 150E, 156E, 157E, 15XE, 15EE, 165E, 167E, 168E, 169E, 176E, 178E, 17EE, 181E, 183E, 184E, 186E, 189E, 18XE, 18EE, 194E, 197E, 19EE, 1X1E, 1X2E, 1X6E, 1XXE, 1E0E, 1E2E, 1E3E, 1E4E, 1E7E, 200E, 202E, 205E, 206E, 211E, 214E, 215E, 219E, 221E, 222E, 224E, 228E, 229E, 231E, 232E, 234E, 239E, 23XE, 243E, 244E, 247E, 248E, 252E, 256E, 257E, 258E, 265E, 26XE, 26EE, 274E, 276E, 279E, 282E, 285E, 286E, 287E, 28EE, 292E, 293E, 299E, 2X1E, 2X2E, 2X3E, 2X5E, 2X8E, 2XEE, 2E0E, 2E3E, 2E4E, 2E8E, 2EXE, 303E, 307E, 309E, 311E, 314E, 315E, 31EE, 320E, 322E, 323E, 324E, 329E, 331E, 332E, 337E, 341E, 343E, 346E, 348E, 349E, 34EE, 351E, 352E, 356E, 358E, 35EE, 366E, 367E, 370E, 375E, 377E, 378E, 379E, 37XE, 381E, 390E, 395E, 396E, 399E, 3X2E, 3X7E, 3E0E, 3E1E, 3E2E, 3E4E, 3E7E, 3EXE, 3EEE, 402E, 403E, 404E, 405E, 408E, 40XE, 411E, 413E, 415E, 417E, 41XE, 420E, 423E, 426E, 428E, 42XE, 438E, 43EE, 440E, 442E, 444E, 445E, 447E, 449E, 450E, 454E, 455E, 457E, 463E, 468E, 46XE, 46EE, 479E, 481E, 483E, 484E, 486E, 488E, 490E, 491E, 492E, 496E, 4X0E, 4X2E, 4X5E, 4X7E, 4E3E, 4EXE, 501E, 504E, 508E, 50EE, 511E, 512E, 513E, 516E, 521E, 522E, 525E, 526E, 52XE, 53XE, 540E, 541E, 547E, 548E, 550E, 554E, 555E, 558E, 559E, 55XE, 562E, 563E, 566E, 569E, 575E, 577E, 579E, 57EE, 580E, 583E, 584E, 587E, 58XE, 595E, 59XE, 59EE, 5X0E, 5X1E, 5X4E, 5X5E, 5X6E, 5XXE, 5XEE, 5E1E, 5E2E, 5E3E, 5E8E, 5E9E, 601E, 604E, 607E, 609E, 60XE, 613E, 617E, 619E, 620E, 622E, 626E, 62EE, 633E, 634E, 636E, 642E, 644E, 646E, 64EE, 655E, 656E, 660E, 663E, 669E, 671E, 672E, 673E, 675E, 677E, 678E, 67EE, 684E, 692E, 699E, 69EE, 6X1E, 6X4E, 6X7E, 6X9E, 6XXE, 6E2E, 6E4E, 6E9E, 700E, 701E, 703E, 708E, 70XE, 70EE, 710E, 711E, 716E, 718E, 727E, 728E, 729E, 72EE, 730E, 736E, 739E, 73XE, 73EE, 745E, 749E, 756E, 757E, 758E, 75EE, 761E, 763E, 766E, 76EE, 771E, 773E, 774E, 776E, 780E, 786E, 789E, 794E, 795E, 797E, 798E, 79XE, 7X6E, 7XEE, 7E0E, 7E5E, 7E6E, 7E9E, 802E, 804E, 806E, 808E, 80EE, 816E, 819E, 823E, 827E, 82XE, 833E, 835E, 83XE, 840E, 841E, 843E, 849E, 84EE, 853E, 856E, 857E, 860E, 862E, 864E, 865E, 866E, 867E, 86EE, 870E, 872E, 873E, 874E, 878E, 879E, 888E, 88XE, 890E, 898E, 89EE, 8X1E, 8X2E, 8X7E, 8X9E, 8E2E, 8E4E, 8E9E, 8EEE, 907E, 909E, 90XE, 912E, 915E, 917E, 918E, 923E, 926E, 929E, 92XE, 931E, 936E, 938E, 939E, 93EE, 940E, 944E, 947E, 953E, 960E, 962E, 965E, 96XE, 973E, 974E, 975E, 97XE, 97EE, 984E, 986E, 988E, 989E, 991E, 992E, 996E, 997E, 99XE, 9X2E, 9X8E, 9XXE, 9E1E, 9E3E, 9E5E, 9E7E, X00E, X03E, X05E, X08E, X13E, X14E, X17E, X20E, X24E, X32E, X35E, X37E, X42E, X43E, X46E, X4XE, X53E, X54E, X59E, X5XE, X5EE, X63E, X68E, X6EE, X71E, X76E, X80E, X85E, X88E, X90E, X97E, X9EE, XX0E, XX1E, XX6E, XX9E, XE2E, XE3E, XE6E, XE7E, E01E, E05E, E0XE, E10E, E14E, E18E, E21E, E26E, E27E, E28E, E2XE, E31E, E39E, E3XE, E3EE, E4EE, E50E, E51E, E52E, E63E, E68E, E69E, E72E, E73E, E78E, E7XE, E81E, E84E, E85E, E91E, E97E, E98E, EX2E, EX4E, EX7E, EE2E, EE3E, EE5E, ...

Prime k-tuple Edit

(p, p+2) (twin primes): (3, 5), (5, 7), (E, 11), (15, 17), (25, 27), (35, 37), (4E, 51), (5E, 61), (85, 87), (8E, 91), (E5, E7), (105, 107), (12E, 131), (13E, 141), (145, 147), (16E, 171), (17E, 181), (1X5, 1X7), (1E5, 1E7), (21E, 221), (24E, 251), (2XE, 2E1), (2EE, 301), (325, 327), (375, 377), (3E5, 3E7), (41E, 421), (435, 437), (455, 457), (46E, 471), (575, 577), (585, 587), (58E, 591), (5E5, 5E7), (615, 617), (70E, 711), (71E, 721), (735, 737), (745, 747), (76E, 771), (7EE, 801), (865, 867), (8X5, 8X7), (8E5, 8E7), (905, 907), (91E, 921), (9XE, 9E1), (X0E, X11), (X35, X37), (X3E, X41), (E1E, E21), (E2E, E31), (E6E, E71), (E95, E97), (EE5, EE7), (104E, 1051), (10EE, 1101), (1105, 1107), (114E, 1151), (1165, 1167), (11X5, 11X7), (120E, 1211), (1255, 1257), (125E, 1261), (127E, 1281), (1295, 1297), (12X5, 12X7), (1365, 1367), (138E, 1391), (1405, 1407), (142E, 1431), (1465, 1467), (1585, 1587), (15EE, 1601), (1655, 1657), (167E, 1681), (169E, 16X1), (16E5, 16E7), (1745, 1747), (1755, 1757), (1875, 1877), (189E, 18X1), (197E, 1981), (19EE, 1X01), (1X6E, 1X71), (1X75, 1X77), (1XXE, 1XE1), (1E15, 1E17), (1E3E, 1E41), (1E4E, 1E51), (1E65, 1E67), (2005, 2007), (200E, 2011), (205E, 2061), (206E, 2071), (2085, 2087), (20X5, 20X7), (215E, 2161), (221E, 2221), (2265, 2267), (228E, 2291), (2325, 2327), (2335, 2337), (2395, 2397), (23XE, 23E1), (2415, 2417), (244E, 2451), (247E, 2481), (24X5, 24X7), (2535, 2537), (2545, 2547), (2555, 2557), (256E, 2571), (257E, 2581), (2615, 2617), (2685, 2687), (2715, 2717), (2745, 2747), (276E, 2771), (2825, 2827), (2835, 2837), (2895, 2897), (292E, 2931), (293E, 2941), (2X2E, 2X31), (2X5E, 2X61), (2X95, 2X97), (2XX5, 2XX7), (2E4E, 2E51), (303E, 3041), (307E, 3081), (3175, 3177), (3195, 3197), (3205, 3207), (3225, 3227), (323E, 3241), (331E, 3321), (332E, 3331), (3335, 3337), (33X5, 33X7), (3475, 3477), (348E, 3491), (349E, 34X1), (3635, 3637), (366E, 3671), (3705, 3707), (3765, 3767), (378E, 3791), (381E, 3821), (3895, 3897), (395E, 3961), (3975, 3977), (3X2E, 3X31), (3X55, 3X57), (3X65, 3X67), (3XE5, 3XE7), (3E0E, 3E11), (3E1E, 3E21), (3E4E, 3E51), (3E85, 3E87), (402E, 4031), (403E, 4041), (415E, 4161), (420E, 4211), (428E, 4291), (42XE, 42E1), (4305, 4307), (4395, 4397), (43EE, 4401), (444E, 4451), (445E, 4461), (4485, 4487), (45X5, 45X7), (4685, 4687), (4725, 4727), (4775, 4777), (481E, 4821), (490E, 4911), (491E, 4921), (496E, 4971), (4X2E, 4X31), (4X65, 4X67), (4E35, 4E37), (4E85, 4E87), (4EXE, 4EE1), (512E, 5131), (5145, 5147), (5165, 5167), (5235, 5237), (525E, 5261), (526E, 5271), (5295, 5297), (541E, 5421), (5455, 5457), (54X5, 54X7), (554E, 5551), (555E, 5561), (5565, 5567), (5585, 5587), (56X5, 56X7), (5725, 5727), (575E, 5761), (579E, 57X1), (5855, 5857), (58E5, 58E7), (595E, 5961), (5985, 5987), (59XE, 59E1), (5X0E, 5X11), (5X4E, 5X51), (5E3E, 5E41), (5E65, 5E67), (5E8E, 5E91), (604E, 6051), (6075, 6077), (60XE, 60E1), (6115, 6117), (6245, 6247), (634E, 6351), (6375, 6377), (63E5, 63E7), (6495, 6497), (64X5, 64X7), (6525, 6527), (655E, 6561), (656E, 6571), (669E, 66X1), (6795, 6797), (6825, 6827), (692E, 6931), (6945, 6947), (6995, 6997), (6X1E, 6X21), (6XXE, 6XE1), (6E15, 6E17), (6E75, 6E77), (6E9E, 6EX1), (700E, 7011), (7055, 7057), (70EE, 7101), (710E, 7111), (71E5, 71E7), (730E, 7311), (736E, 7371), (7505, 7507), (7585, 7587), (7635, 7637), (763E, 7641), (7795, 7797), (7875, 7877), (7905, 7907), (7XEE, 7E01), (7E0E, 7E11), (7E25, 7E27), (7E35, 7E37), (7E65, 7E67), (8005, 8007), (8045, 8047), (8065, 8067), (808E, 8091), (8125, 8127), (8135, 8137), (8195, 8197), (82E5, 82E7), (8355, 8357), (83XE, 83E1), (843E, 8441), (8505, 8507), (8515, 8517), (853E, 8541), (856E, 8571), (872E, 8731), (8915, 8917), (8X05, 8X07), (8X1E, 8X21), (8X55, 8X57), (8X7E, 8X81), (9025, 9027), (9075, 9077), (907E, 9081), (912E, 9131), (9135, 9137), (923E, 9241), (92XE, 92E1), (9365, 9367), (936E, 9371), (940E, 9411), (944E, 9451), (9485, 9487), (9575, 9577), (962E, 9631), (975E, 9761), (9775, 9777), (97XE, 97E1), (98X5, 98X7), (9945, 9947), (99XE, 99E1), (9X2E, 9X31), (9E45, 9E47), (9E5E, 9E61), (X00E, X011), (X08E, X091), (X0E5, X0E7), (X155, X157), (X20E, X211), (X225, X227), (X275, X277), (X295, X297), (X32E, X331), (X365, X367), (X3X5, X3X7), (X445, X447), (X455, X457), (X485, X487), (X4XE, X4E1), (X535, X537), (X53E, X541), (X54E, X551), (X59E, X5X1), (X5XE, X5E1), (X68E, X691), (X6EE, X701), (X71E, X721), (X875, X877), (X88E, X891), (XE3E, XE41), (XE45, XE47), (E05E, E061), (E0XE, E0E1), (E125, E127), (E14E, E151), (E26E, E271), (E2X5, E2X7), (E2XE, E2E1), (E325, E327), (E385, E387), (E495, E497), (E51E, E521), (E595, E597), (E615, E617), (E675, E677), (E69E, E6X1), (E705, E707), (E7XE, E7E1), (E85E, E861), (E945, E947), (E9E5, E9E7), (EX25, EX27), (EX4E, EX51), (EX85, EX87), (EE3E, EE41), (EEX5, EEX7), ...

(p, p+4) (cousin primes): (3, 7), (7, E), (11, 15), (17, 1E), (31, 35), (37, 3E), (57, 5E), (67, 6E), (81, 85), (87, 8E), (91, 95), (X7, XE), (117, 11E), (141, 145), (167, 16E), (171, 175), (1E1, 1E5), (217, 21E), (221, 225), (251, 255), (277, 27E), (291, 295), (307, 30E), (321, 325), (327, 32E), (347, 34E), (357, 35E), (431, 435), (457, 45E), (481, 485), (517, 51E), (531, 535), (541, 545), (587, 58E), (5E1, 5E5), (5E7, 5EE), (611, 615), (617, 61E), (637, 63E), (661, 665), (687, 68E), (701, 705), (767, 76E), (771, 775), (851, 855), (8X7, 8XE), (901, 905), (907, 90E), (9X7, 9XE), (9E1, 9E5), (X07, X0E), (X37, X3E), (X41, X45), (X91, X95), (XX7, XXE), (XE7, XEE), (E11, E15), (E21, E25), (E67, E6E), (E91, E95), (1047, 104E), (10E7, 10EE), (1101, 1105), (11X1, 11X5), (11X7, 11XE), (1257, 125E), (12X1, 12X5), (1337, 133E), (1367, 136E), (1391, 1395), (13E1, 13E5), (1437, 143E), (1461, 1465), (1471, 1475), (14E1, 14E5), (1521, 1525), (1577, 157E), (1621, 1625), (1657, 165E), (1677, 167E), (1681, 1685), (1697, 169E), (1711, 1715), (1751, 1755), (1781, 1785), (17X1, 17X5), (1861, 1865), (18E7, 18EE), (1911, 1915), (1947, 194E), (19E7, 19EE), (1X17, 1X1E), (1X41, 1X45), (1X71, 1X75), (1E07, 1E0E), (1E27, 1E2E), (2001, 2005), (2007, 200E), (2061, 2065), (2111, 2115), (2161, 2165), (2181, 2185), (2241, 2245), (2287, 228E), (22E1, 22E5), (2317, 231E), (2327, 232E), (2347, 234E), (2397, 239E), (2481, 2485), (24X1, 24X5), (26X7, 26XE), (2741, 2745), (2747, 274E), (2827, 282E), (28X1, 28X5), (2927, 292E), (2931, 2935), (2951, 2955), (2X31, 2X35), (2X61, 2X65), (2X87, 2X8E), (2E31, 2E35), (2EX7, 2EXE), (3037, 303E), (3041, 3045), (3117, 311E), (3171, 3175), (3191, 3195), (3207, 320E), (3227, 322E), (3247, 324E), (3281, 3285), (3327, 332E), (3331, 3335), (3361, 3365), (33X1, 33X5), (3417, 341E), (3467, 346E), (3481, 3485), (3517, 351E), (3587, 358E), (35E7, 35EE), (3707, 370E), (3721, 3725), (38E1, 38E5), (3957, 395E), (3981, 3985), (3X91, 3X95), (3E47, 3E4E), (3E51, 3E55), (3EE7, 3EEE), (4047, 404E), (4071, 4075), (40X7, 40XE), (4207, 420E), (4237, 423E), (43E1, 43E5), (4441, 4445), (4471, 4475), (4497, 449E), (4507, 450E), (4531, 4535), (4547, 454E), (4557, 455E), (4577, 457E), (45X1, 45X5), (4611, 4615), (4681, 4685), (4687, 468E), (4711, 4715), (4821, 4825), (4887, 488E), (4921, 4925), (4951, 4955), (4967, 496E), (4971, 4975), (4X57, 4X5E), (4X77, 4X7E), (4E37, 4E3E), (4EX7, 4EXE), (5031, 5035), (5041, 5045), (5081, 5085), (50E7, 50EE), (5117, 511E), (5167, 516E), (5201, 5205), (5267, 526E), (5351, 5355), (5371, 5375), (53X7, 53XE), (5451, 5455), (5487, 548E), (54X1, 54X5), (5561, 5565), (5587, 558E), (5637, 563E), (5697, 569E), (5777, 577E), (57E7, 57EE), (5831, 5835), (5877, 587E), (5X17, 5X1E), (5X67, 5X6E), (5X81, 5X85), (5E17, 5E1E), (5E37, 5E3E), (5E91, 5E95), (6051, 6055), (6071, 6075), (6077, 607E), (6171, 6175), (6197, 619E), (6207, 620E), (6227, 622E), (6261, 6265), (64E7, 64EE), (6521, 6525), (6571, 6575), (6607, 660E), (6621, 6625), (6671, 6675), (6757, 675E), (6777, 677E), (6861, 6865), (6881, 6885), (6911, 6915), (6997, 699E), (6X17, 6X1E), (6X47, 6X4E), (6X97, 6X9E), (6E47, 6E4E), (6E71, 6E75), (7001, 7005), (7011, 7015), (7051, 7055), (7131, 7135), (7187, 718E), (71E1, 71E5), (7221, 7225), (7241, 7245), (7287, 728E), (7391, 7395), (7457, 745E), (7561, 7565), (7577, 757E), (7587, 758E), (7617, 761E), (7637, 763E), (7661, 7665), (76E7, 76EE), (7737, 773E), (7747, 774E), (7767, 776E), (7851, 7855), (7867, 786E), (7921, 7925), (7E07, 7E0E), (7E11, 7E15), (7E67, 7E6E), (8041, 8045), (8047, 804E), (8067, 806E), (80E7, 80EE), (8151, 8155), (8197, 819E), (8231, 8235), (8251, 8255), (8357, 835E), (8407, 840E), (8417, 841E), (84E1, 84E5), (8511, 8515), (8571, 8575), (8591, 8595), (8621, 8625), (8641, 8645), (8667, 866E), (8677, 867E), (86E7, 86EE), (8747, 874E), (8797, 879E), (8831, 8835), (8881, 8885), (89E7, 89EE), (8X91, 8X95), (8E27, 8E2E), (8E71, 8E75), (9077, 907E), (9097, 909E), (90X7, 90XE), (9127, 912E), (9131, 9135), (9177, 917E), (9231, 9235), (9267, 926E), (9361, 9365), (9367, 936E), (9371, 9375), (9387, 938E), (9447, 944E), (9451, 9455), (94X1, 94X5), (9601, 9605), (9627, 962E), (9651, 9655), (9737, 973E), (9781, 9785), (97E7, 97EE), (9847, 984E), (9927, 992E), (9967, 996E), (9X31, 9X35), (9E57, 9E5E), (X031, X035), (X087, X08E), (X091, X095), (X137, X13E), (X201, X205), (X247, X24E), (X4X1, X4X5), (X537, X53E), (X5X7, X5XE), (X671, X675), (X691, X695), (X717, X71E), (X767, X76E), (X791, X795), (X807, X80E), (X821, X825), (X871, X875), (X907, X90E), (XX61, XX65), (XE41, XE45), (E001, E005), (E051, E055), (E147, E14E), (E277, E27E), (E2X1, E2X5), (E2X7, E2XE), (E2E1, E2E5), (E527, E52E), (E6X1, E6X5), (E727, E72E), (E781, E785), (E7X7, E7XE), (E811, E815), (E917, E91E), (E941, E945), (E971, E975), (E987, E98E), (EX27, EX2E), ...

(p, p+6) (sexy primes): (5, E), (7, 11), (E, 15), (11, 17), (15, 1E), (1E, 25), (27, 31), (31, 37), (35, 3E), (3E, 45), (45, 4E), (51, 57), (57, 61), (61, 67), (6E, 75), (81, 87), (85, 8E), (87, 91), (8E, 95), (XE, E5), (107, 111), (111, 117), (11E, 125), (125, 12E), (13E, 145), (141, 147), (167, 171), (16E, 175), (175, 17E), (18E, 195), (195, 19E), (19E, 1X5), (1X7, 1E1), (1E1, 1E7), (217, 221), (21E, 225), (237, 241), (24E, 255), (255, 25E), (267, 271), (271, 277), (27E, 285), (301, 307), (30E, 315), (321, 327), (325, 32E), (35E, 365), (391, 397), (3X5, 3XE), (3XE, 3E5), (3E7, 401), (40E, 415), (415, 41E), (421, 427), (427, 431), (431, 437), (455, 45E), (45E, 465), (465, 46E), (485, 48E), (507, 511), (511, 517), (527, 531), (585, 58E), (587, 591), (5E1, 5E7), (5E5, 5EE), (611, 617), (615, 61E), (665, 66E), (66E, 675), (68E, 695), (695, 69E), (6X7, 6E1), (705, 70E), (721, 727), (747, 751), (767, 771), (76E, 775), (775, 77E), (77E, 785), (791, 797), (797, 7X1), (825, 82E), (82E, 835), (855, 85E), (85E, 865), (867, 871), (8X5, 8XE), (8XE, 8E5), (8E7, 901), (901, 907), (905, 90E), (921, 927), (955, 95E), (95E, 965), (9X7, 9E1), (9XE, 9E5), (9E5, 9EE), (X07, X11), (X11, X17), (X35, X3E), (X37, X41), (X3E, X45), (X45, X4E), (X87, X91), (X95, X9E), (E15, E1E), (E1E, E25), (E25, E2E), (E31, E37), (E61, E67), (E67, E71), (E91, E97), (1011, 1017), (1017, 1021), (1021, 1027), (1041, 1047), (1047, 1051), (10E1, 10E7), (10E7, 1101), (10EE, 1105), (1101, 1107), (1125, 112E), (112E, 1135), (1185, 118E), (1197, 11X1), (11X1, 11X7), (11X5, 11XE), (11E7, 1201), (123E, 1245), (1255, 125E), (1257, 1261), (1297, 12X1), (12X1, 12X7), (133E, 1345), (1365, 136E), (138E, 1395), (13X1, 13X7), (13X7, 13E1), (1425, 142E), (1431, 1437), (143E, 1445), (1457, 1461), (1461, 1467), (1467, 1471), (1475, 147E), (148E, 1495), (1495, 149E), (14E5, 14EE), (1517, 1521), (157E, 1585), (1587, 1591), (1655, 165E), (1667, 1671), (1671, 1677), (1677, 1681), (167E, 1685), (1685, 168E), (1697, 16X1), (16X1, 16X7), (1747, 1751), (1751, 1757), (1785, 178E), (1797, 17X1), (1815, 181E), (181E, 1825), (1865, 186E), (186E, 1875), (1931, 1937), (194E, 1955), (19E7, 1X01), (1X11, 1X17), (1X2E, 1X35), (1X6E, 1X75), (1X71, 1X77), (1XE1, 1XE7), (1XE7, 1E01), (1E01, 1E07), (1E0E, 1E15), (1E7E, 1E85), (2001, 2007), (2005, 200E), (2007, 2011), (2047, 2051), (205E, 2065), (2065, 206E), (2071, 2077), (2107, 2111), (2115, 211E), (2127, 2131), (2131, 2137), (215E, 2165), (2177, 2181), (21X7, 21E1), (21E1, 21E7), (2215, 221E), (2245, 224E), (2287, 2291), (231E, 2325), (2325, 232E), (232E, 2335), (2395, 239E), (239E, 23X5), (23X5, 23XE), (23E1, 23E7), (2417, 2421), (2435, 243E), (2451, 2457), (247E, 2485), (2485, 248E), (24X1, 24X7), (252E, 2535), (2565, 256E), (258E, 2595), (2631, 2637), (265E, 2665), (26X1, 26X7), (26XE, 26E5), (26E5, 26EE), (2737, 2741), (2741, 2747), (2745, 274E), (2781, 2787), (27X7, 27E1), (27E1, 27E7), (2825, 282E), (282E, 2835), (2837, 2841), (2841, 2847), (2855, 285E), (2897, 28X1), (2927, 2931), (292E, 2935), (2935, 293E), (299E, 29X5), (2X07, 2X11), (2X2E, 2X35), (2X35, 2X3E), (2X47, 2X51), (2X5E, 2X65), (2X77, 2X81), (2X81, 2X87), (2X8E, 2X95), (2E35, 2E3E), (2E51, 2E57), (2E57, 2E61), (2E61, 2E67), (2E8E, 2E95), (3037, 3041), (303E, 3045), (3075, 307E), (3095, 309E), (309E, 30X5), (3145, 314E), (314E, 3155), (3155, 315E), (3167, 3171), (3171, 3177), (3187, 3191), (3191, 3197), (3197, 31X1), (31EE, 3205), (3205, 320E), (3225, 322E), (3241, 3247), (3271, 3277), (3277, 3281), (3321, 3327), (3327, 3331), (332E, 3335), (3331, 3337), (3357, 3361), (337E, 3385), (33X1, 33X7), (33X7, 33E1), (3435, 343E), (343E, 3445), (3451, 3457), (346E, 3475), (3477, 3481), (3485, 348E), (34E5, 34EE), (3565, 356E), (35E1, 35E7), (35EE, 3605), (3617, 3621), (3621, 3627), (3705, 370E), (3717, 3721), (3755, 375E), (375E, 3765), (3767, 3771), (379E, 37X5), (37X5, 37XE), (37XE, 37E5), (3801, 3807), (3815, 381E), (3821, 3827), (3827, 3831), (3831, 3837), (3871, 3877), (3957, 3961), (396E, 3975), (3977, 3981), (3X25, 3X2E), (3X41, 3X47), (3X67, 3X71), (3E47, 3E51), (3E4E, 3E55), (3E75, 3E7E), (3E7E, 3E85), (3EEE, 4005), (4041, 4047), (404E, 4055), (4055, 405E), (4067, 4071), (4085, 408E), (413E, 4145), (4155, 415E), (41XE, 41E5), (4207, 4211), (4211, 4217), (4231, 4237), (423E, 4245), (4357, 4361), (438E, 4395), (43E5, 43EE), (4425, 442E), (442E, 4435), (4445, 444E), (4475, 447E), (447E, 4485), (450E, 4515), (4541, 4547), (4571, 4577), (45X1, 45X7), (4635, 463E), (463E, 4645), (4677, 4681), (4681, 4687), (4685, 468E), (46X5, 46XE), (4707, 4711), (4777, 4781), (47E1, 47E7), (4815, 481E), (481E, 4825), (483E, 4845), (4845, 484E), (4881, 4887), (491E, 4925), (4925, 492E), (4947, 4951), (4967, 4971), (496E, 4975), (4987, 4991), (4X0E, 4X15), (4X5E, 4X65), (4X91, 4X97), (4E21, 4E27), (4E35, 4E3E), (4EX7, 4EE1), (5001, 5007), (501E, 5025), (5045, 504E), (5057, 5061), (5061, 5067), (5077, 5081), (5085, 508E), (508E, 5095), (513E, 5145), (5165, 516E), (5187, 5191), (51E7, 5201), (522E, 5235), (5261, 5267), (5267, 5271), (5297, 52X1), (5327, 5331), (5347, 5351), (5367, 5371), (5391, 5397), (53XE, 53E5), (5405, 540E), (5451, 5457), (54X1, 54X7), (54X7, 54E1), (550E, 5515), (5527, 5531), (5531, 5537), (5545, 554E), (555E, 5565), (5561, 5567), (5585, 558E), (558E, 5595), (5595, 559E), (55XE, 55E5), (5625, 562E), (5691, 5697), (569E, 56X5), (56E7, 5701), (5771, 5777), (577E, 5785), (57E1, 57E7), (5817, 5821), (5835, 583E), (584E, 5855), (5891, 5897), (58XE, 58E5), (5927, 5931), (59X5, 59XE), (5X11, 5X17), (5X45, 5X4E), (5X6E, 5X75), (5E1E, 5E25), (5E25, 5E2E), (5E37, 5E41), (5E8E, 5E95), (5E95, 5E9E), (604E, 6055), (6071, 6077), (6075, 607E), (6175, 617E), (617E, 6185), (61E7, 6201), (6201, 6207), (6257, 6261), (6265, 626E), (6327, 6331), (633E, 6345), (6345, 634E), (6351, 6357), (636E, 6375), (6387, 6391), (6425, 642E), (6437, 6441), (64EE, 6505), (6521, 6527), (656E, 6575), (6617, 6621), (6635, 663E), (6667, 6671), (6715, 671E), (6751, 6757), (678E, 6795), (6797, 67X1), (67X1, 67X7), (6857, 6861), (6995, 699E), (699E, 69X5), (69E5, 69EE), (69EE, 6X05), (6X11, 6X17), (6X17, 6X21), (6X21, 6X27), (6X75, 6X7E), (6X7E, 6X85), (6X9E, 6XX5), (6XX5, 6XXE), (6E01, 6E07), (6E25, 6E2E), (6E71, 6E77), (6E77, 6E81), (7005, 700E), (700E, 7015), (7015, 701E), (703E, 7045), (7051, 7057), (7085, 708E), (711E, 7125), (716E, 7175), (71E1, 71E7), (7257, 7261), (7275, 727E), (728E, 7295), (7295, 729E), (72X7, 72E1), (7311, 7317), (7317, 7321), (7341, 7347), (7347, 7351), (7371, 7377), (7395, 739E), (739E, 73X5), (73X5, 73XE), (7421, 7427), (7471, 7477), (7507, 7511), (7565, 756E), (757E, 7585), (7585, 758E), (75E5, 75EE), (7607, 7611), (7611, 7617), (7635, 763E), (7637, 7641), (7665, 766E), (766E, 7675), (76E1, 76E7), (76EE, 7705), (7715, 771E), (7757, 7761), (7761, 7767), (7837, 7841), (786E, 7875), (7917, 7921), (794E, 7955), (7955, 795E), (795E, 7965), (7X47, 7X51), (7X65, 7X6E), (7X77, 7X81), (7E01, 7E07), (7E07, 7E11), (7E0E, 7E15), (7E37, 7E41), (7E5E, 7E65), (7E65, 7E6E), (8041, 8047), (8045, 804E), (8065, 806E), (806E, 8075), (816E, 8175), (8195, 819E), (8227, 8231), (8235, 823E), (82XE, 82E5), (8355, 835E), (8371, 8377), (8401, 8407), (8427, 8431), (84E5, 84EE), (84EE, 8505), (8507, 8511), (8511, 8517), (8565, 856E), (856E, 8575), (8575, 857E), (8625, 862E), (8637, 8641), (8645, 864E), (864E, 8655), (8655, 865E), (86E1, 86E7), (874E, 8755), (8777, 8781), (879E, 87X5), (8885, 888E), (88X5, 88XE), (890E, 8915), (8957, 8961), (8961, 8967), (898E, 8995), (89EE, 8X05), (8X07, 8X11), (8X37, 8X41), (8X41, 8X47), (8X95, 8X9E), (8E45, 8E4E), (8E4E, 8E55), (9041, 9047), (9075, 907E), (9077, 9081), (9091, 9097), (9127, 9131), (912E, 9135), (9131, 9137), (9155, 915E), (915E, 9165), (917E, 9185), (9185, 918E), (918E, 9195), (91X1, 91X7), (9235, 923E), (9251, 9257), (9257, 9261), (9261, 9267), (9315, 931E), (9361, 9367), (9365, 936E), (9367, 9371), (936E, 9375), (938E, 9395), (9395, 939E), (9447, 9451), (944E, 9455), (9475, 947E), (947E, 9485), (94E7, 9501), (9551, 9557), (9577, 9581), (95E7, 9601), (9605, 960E), (960E, 9615), (9627, 9631), (9655, 965E), (965E, 9665), (96XE, 96E5), (9701, 9707), (9707, 9711), (9777, 9781), (97E1, 97E7), (9831, 9837), (989E, 98X5), (992E, 9935), (9961, 9967), (996E, 9975), (9975, 997E), (99E1, 99E7), (99E7, 9X01), (9X25, 9X2E), (9X2E, 9X35), (9X41, 9X47), (9X47, 9X51), (9X85, 9X8E), (9XX5, 9XXE), (9E3E, 9E45), (9E57, 9E61), (X011, X017), (X035, X03E), (X03E, X045), (X081, X087), (X087, X091), (X08E, X095), (X117, X121), (X13E, X145), (X145, X14E), (X14E, X155), (X157, X161), (X205, X20E), (X2E7, X301), (X35E, X365), (X43E, X445), (X457, X461), (X497, X4X1), (X4X5, X4XE), (X535, X53E), (X537, X541), (X5X1, X5X7), (X5X7, X5E1), (X5EE, X605), (X657, X661), (X661, X667), (X667, X671), (X68E, X695), (X711, X717), (X717, X721), (X7E7, X801), (X801, X807), (X817, X821), (X871, X877), (X90E, X915), (X9E5, X9EE), (XX1E, XX25), (XX57, XX61), (XX65, XX6E), (XE3E, XE45), (XE41, XE47), (XE91, XE97), (E01E, E025), (E055, E05E), (E061, E067), (E105, E10E), (E147, E151), (E151, E157), (E167, E171), (E197, E1X1), (E265, E26E), (E271, E277), (E2X1, E2X7), (E2X5, E2XE), (E2X7, E2E1), (E2XE, E2E5), (E301, E307), (E315, E31E), (E31E, E325), (E327, E331), (E331, E337), (E337, E341), (E351, E357), (E395, E39E), (E3XE, E3E5), (E3E5, E3EE), (E411, E417), (E417, E421), (E481, E487), (E521, E527), (E571, E577), (E5E1, E5E7), (E635, E63E), (E685, E68E), (E69E, E6X5), (E707, E711), (E771, E777), (E777, E781), (E785, E78E), (E78E, E795), (E7X7, E7E1), (E815, E81E), (E91E, E925), (E931, E937), (E937, E941), (E941, E947), (E975, E97E), (EX25, EX2E), (EX7E, EX85), (EE01, EE07), ...

(p, p+8) (octy primes): (3, E), (5, 11), (E, 17), (1E, 27), (25, 31), (45, 51), (4E, 57), (5E, 67), (75, 81), (85, 91), (XE, E7), (105, 111), (125, 131), (13E, 147), (175, 181), (19E, 1X7), (1X5, 1E1), (25E, 267), (285, 291), (295, 2X1), (2EE, 307), (315, 321), (33E, 347), (34E, 357), (3XE, 3E7), (3E5, 401), (415, 421), (41E, 427), (465, 471), (48E, 497), (4X5, 4E1), (4EE, 507), (51E, 527), (535, 541), (585, 591), (63E, 647), (655, 661), (69E, 6X7), (705, 711), (71E, 727), (745, 751), (785, 791), (80E, 817), (835, 841), (85E, 867), (865, 871), (8XE, 8E7), (8E5, 901), (91E, 927), (965, 971), (9EE, X07), (X0E, X17), (X35, X41), (X6E, X77), (X9E, XX7), (XXE, XE7), (E15, E21), (E25, E31), (E2E, E37), (1005, 1011), (107E, 1087), (10EE, 1107), (118E, 1197), (11XE, 11E7), (1255, 1261), (1295, 12X1), (12E5, 1301), (1345, 1351), (136E, 1377), (1395, 13X1), (1425, 1431), (142E, 1437), (1465, 1471), (150E, 1517), (156E, 1577), (157E, 1587), (1585, 1591), (1615, 1621), (165E, 1667), (168E, 1697), (169E, 16X7), (1705, 1711), (1745, 1751), (178E, 1797), (17EE, 1807), (1825, 1831), (186E, 1877), (18XE, 18E7), (1915, 1921), (1X35, 1X41), (1X45, 1X51), (1X6E, 1X77), (1XXE, 1XE7), (1E0E, 1E17), (1EE5, 2001), (2005, 2011), (202E, 2037), (2065, 2071), (206E, 2077), (211E, 2127), (2185, 2191), (219E, 21X7), (2215, 2221), (22E5, 2301), (231E, 2327), (232E, 2337), (23X5, 23E1), (23XE, 23E7), (2415, 2421), (244E, 2457), (252E, 2537), (2565, 2571), (2595, 25X1), (2625, 2631), (279E, 27X7), (282E, 2837), (2835, 2841), (2895, 28X1), (28EE, 2907), (2935, 2941), (2X3E, 2X47), (2X8E, 2X97), (2E0E, 2E17), (2E4E, 2E57), (2EXE, 2EE7), (3005, 3011), (3075, 3081), (315E, 3167), (3195, 31X1), (31EE, 3207), (323E, 3247), (3285, 3291), (331E, 3327), (332E, 3337), (3365, 3371), (33X5, 33E1), (341E, 3427), (3445, 3451), (346E, 3477), (3475, 3481), (3485, 3491), (35X5, 35E1), (3655, 3661), (367E, 3687), (370E, 3717), (3725, 3731), (375E, 3767), (3765, 3771), (37E5, 3801), (3815, 3821), (381E, 3827), (3845, 3851), (38E5, 3901), (3935, 3941), (396E, 3977), (3975, 3981), (399E, 39X7), (3X25, 3X31), (3X65, 3X71), (3E55, 3E61), (3E7E, 3E87), (3EXE, 3EE7), (403E, 4047), (405E, 4067), (408E, 4097), (4155, 4161), (417E, 4187), (420E, 4217), (4225, 4231), (438E, 4397), (43E5, 4401), (440E, 4417), (4435, 4441), (4445, 4451), (447E, 4487), (4535, 4541), (454E, 4557), (46EE, 4707), (4775, 4781), (4815, 4821), (4825, 4831), (488E, 4897), (4X15, 4X21), (4X5E, 4X67), (4E15, 4E21), (4E65, 4E71), (5025, 5031), (5035, 5041), (504E, 5057), (5095, 50X1), (513E, 5147), (5205, 5211), (522E, 5237), (525E, 5267), (5295, 52X1), (52XE, 52E7), (5385, 5391), (547E, 5487), (54X5, 54E1), (5545, 5551), (555E, 5567), (562E, 5637), (569E, 56X7), (5735, 5741), (580E, 5817), (584E, 5857), (58XE, 58E7), (5905, 5911), (59X5, 59E1), (5X0E, 5X17), (5X1E, 5X27), (5X45, 5X51), (5X5E, 5X67), (5X75, 5X81), (5E2E, 5E37), (5E75, 5E81), (601E, 6027), (613E, 6147), (6165, 6171), (619E, 61X7), (62X5, 62E1), (6345, 6351), (634E, 6357), (636E, 6377), (6405, 6411), (642E, 6437), (660E, 6617), (663E, 6647), (6675, 6681), (678E, 6797), (6795, 67X1), (67EE, 6807), (684E, 6857), (6915, 6921), (6X05, 6X11), (6X1E, 6X27), (6XX5, 6XE1), (6E75, 6E81), (7005, 7011), (7045, 7051), (708E, 7097), (7125, 7131), (7135, 7141), (7215, 7221), (7225, 7231), (727E, 7287), (729E, 72X7), (730E, 7317), (7335, 7341), (736E, 7377), (7415, 7421), (7435, 7441), (749E, 74X7), (7505, 7511), (756E, 7577), (757E, 7587), (75EE, 7607), (7635, 7641), (773E, 7747), (774E, 7757), (77E5, 7801), (780E, 7817), (786E, 7877), (7965, 7971), (7X6E, 7X77), (7XEE, 7E07), (7E35, 7E41), (7E5E, 7E67), (7E85, 7E91), (7E9E, 7EX7), (8075, 8081), (82XE, 82E7), (840E, 8417), (841E, 8427), (84EE, 8507), (8505, 8511), (8565, 8571), (862E, 8637), (865E, 8667), (866E, 8677), (86X5, 86E1), (870E, 8717), (873E, 8747), (878E, 8797), (8865, 8871), (888E, 8897), (890E, 8917), (8995, 89X1), (89EE, 8X07), (8X05, 8X11), (8X2E, 8X37), (8X9E, 8XX7), (8E2E, 8E37), (8EEE, 9007), (9075, 9081), (909E, 90X7), (912E, 9137), (9195, 91X1), (9235, 9241), (9365, 9371), (939E, 93X7), (947E, 9487), (9575, 9581), (96E5, 9701), (9775, 9781), (97XE, 97E7), (989E, 98X7), (991E, 9927), (99XE, 99E7), (9X25, 9X31), (9X35, 9X41), (9X8E, 9X97), (9E1E, 9E27), (9E3E, 9E47), (9E7E, 9E87), (X00E, X017), (X045, X051), (X05E, X067), (X095, X0X1), (X14E, X157), (X155, X161), (X205, X211), (X315, X321), (X35E, X367), (X43E, X447), (X455, X461), (X4X5, X4E1), (X535, X541), (X575, X581), (X59E, X5X7), (X63E, X647), (X76E, X777), (X80E, X817), (X97E, X987), (XX25, XX31), (XE3E, XE47), (XEE5, E001), (E055, E061), (E05E, E067), (E14E, E157), (E18E, E197), (E205, E211), (E265, E271), (E26E, E277), (E2X5, E2E1), (E2E5, E301), (E31E, E327), (E325, E331), (E4X5, E4E1), (E51E, E527), (E555, E561), (E5X5, E5E1), (E63E, E647), (E705, E711), (E73E, E747), (E885, E891), (E925, E931), (E97E, E987), (EX7E, EX87), ...

(p, p+X) (dekry primes): (3, 11), (7, 15), (11, 1E), (17, 25), (27, 35), (31, 3E), (37, 45), (51, 5E), (61, 6E), (67, 75), (81, 8E), (87, 95), (X7, E5), (E7, 105), (111, 11E), (117, 125), (131, 13E), (167, 175), (171, 17E), (181, 18E), (1X7, 1E5), (1E7, 205), (217, 225), (241, 24E), (251, 25E), (271, 27E), (277, 285), (2X1, 2XE), (2E1, 2EE), (301, 30E), (307, 315), (321, 32E), (357, 365), (397, 3X5), (401, 40E), (427, 435), (447, 455), (457, 465), (481, 48E), (497, 4X5), (4E1, 4EE), (511, 51E), (527, 535), (557, 565), (577, 585), (591, 59E), (5E1, 5EE), (611, 61E), (647, 655), (661, 66E), (687, 695), (701, 70E), (711, 71E), (727, 735), (737, 745), (767, 775), (771, 77E), (801, 80E), (817, 825), (851, 85E), (881, 88E), (8X7, 8E5), (8E7, 905), (901, 90E), (987, 995), (9X7, 9E5), (9E1, 9EE), (X27, X35), (X37, X45), (X41, X4E), (X87, X95), (X91, X9E), (E11, E1E), (E21, E2E), (E37, E45), (E61, E6E), (E97, EX5), (EE7, 1005), (1041, 104E), (1061, 106E), (10E1, 10EE), (10E7, 1105), (1107, 1115), (1197, 11X5), (11X1, 11XE), (1201, 120E), (1211, 121E), (1231, 123E), (1261, 126E), (1297, 12X5), (12X7, 12E5), (1337, 1345), (13X7, 13E5), (1431, 143E), (1437, 1445), (1457, 1465), (1467, 1475), (1471, 147E), (14E1, 14EE), (1517, 1525), (1561, 156E), (1577, 1585), (1647, 1655), (1671, 167E), (1677, 1685), (1681, 168E), (16X7, 16E5), (16E7, 1705), (1727, 1735), (1747, 1755), (1781, 178E), (1797, 17X5), (1807, 1815), (1831, 183E), (1861, 186E), (18X1, 18XE), (1947, 1955), (1971, 197E), (1X11, 1X1E), (1E01, 1E0E), (1E07, 1E15), (1E41, 1E4E), (2001, 200E), (2051, 205E), (2061, 206E), (2077, 2085), (2097, 20X5), (20X7, 20E5), (2107, 2115), (2111, 211E), (2177, 2185), (2191, 219E), (2221, 222E), (2241, 224E), (2267, 2275), (2291, 229E), (2317, 2325), (2327, 2335), (2397, 23X5), (2481, 248E), (2521, 252E), (2537, 2545), (2547, 2555), (2557, 2565), (2571, 257E), (2581, 258E), (2607, 2615), (2617, 2625), (2637, 2645), (26X1, 26XE), (26X7, 26E5), (2717, 2725), (2737, 2745), (2741, 274E), (2827, 2835), (2847, 2855), (2897, 28X5), (2927, 2935), (2931, 293E), (2991, 299E), (2X11, 2X1E), (2X31, 2X3E), (2X51, 2X5E), (2X81, 2X8E), (2X87, 2X95), (2X97, 2XX5), (2E31, 2E3E), (2EE7, 3005), (3037, 3045), (30E7, 3105), (3167, 3175), (3187, 3195), (3241, 324E), (3277, 3285), (3291, 329E), (3321, 332E), (3327, 3335), (3337, 3345), (3357, 3365), (3371, 337E), (3427, 3435), (3467, 3475), (3477, 3485), (3481, 348E), (3491, 349E), (35E1, 35EE), (35E7, 3605), (3627, 3635), (3637, 3645), (3661, 366E), (3671, 367E), (3697, 36X5), (3717, 3725), (3747, 3755), (3771, 377E), (3791, 379E), (3807, 3815), (3837, 3845), (3901, 390E), (3961, 396E), (3977, 3985), (3X47, 3X55), (3X57, 3X65), (3X71, 3X7E), (3E11, 3E1E), (3E21, 3E2E), (3E47, 3E55), (3EE7, 4005), (4031, 403E), (4041, 404E), (4047, 4055), (4067, 4075), (4111, 411E), (41X1, 41XE), (4217, 4225), (4231, 423E), (4237, 4245), (4281, 428E), (42X1, 42XE), (43E1, 43EE), (4401, 440E), (4417, 4425), (4441, 444E), (4451, 445E), (4471, 447E), (4507, 4515), (4541, 454E), (4571, 457E), (4677, 4685), (4681, 468E), (4707, 4715), (47E7, 4805), (4831, 483E), (4881, 488E), (4901, 490E), (4911, 491E), (4921, 492E), (4947, 4955), (4967, 4975), (4X01, 4X0E), (4X21, 4X2E), (4X57, 4X65), (4E27, 4E35), (4E57, 4E65), (4E87, 4E95), (5041, 504E), (5077, 5085), (5081, 508E), (5131, 513E), (5147, 5155), (51E7, 5205), (5211, 521E), (5261, 526E), (52X1, 52XE), (5347, 5355), (5367, 5375), (53X7, 53E5), (5457, 5465), (5537, 5545), (5551, 555E), (5587, 5595), (5607, 5615), (5691, 569E), (5697, 56X5), (5727, 5735), (5771, 577E), (5777, 5785), (57E1, 57EE), (5831, 583E), (58E7, 5905), (59E1, 59EE), (5X11, 5X1E), (5X51, 5X5E), (5X67, 5X75), (5E17, 5E25), (5E67, 5E75), (5E81, 5E8E), (5E91, 5E9E), (6071, 607E), (6091, 609E), (6171, 617E), (6201, 620E), (6257, 6265), (6261, 626E), (6297, 62X5), (62E1, 62EE), (6331, 633E), (63E7, 6405), (6441, 644E), (6487, 6495), (6497, 64X5), (64E7, 6505), (6551, 655E), (6561, 656E), (6617, 6625), (6667, 6675), (6707, 6715), (6751, 675E), (6857, 6865), (6921, 692E), (6997, 69X5), (6X11, 6X1E), (6X67, 6X75), (6X97, 6XX5), (6E07, 6E15), (6E17, 6E25), (7001, 700E), (7011, 701E), (7101, 710E), (7111, 711E), (7207, 7215), (7287, 7295), (72E1, 72EE), (7361, 736E), (7391, 739E), (7427, 7435), (7491, 749E), (74X7, 74E5), (7561, 756E), (7577, 7585), (7611, 761E), (7661, 766E), (76E1, 76EE), (76E7, 7705), (7761, 776E), (7797, 77X5), (7801, 780E), (7867, 7875), (7917, 7925), (7941, 794E), (7971, 797E), (79X1, 79XE), (7X27, 7X35), (7XE1, 7XEE), (7E01, 7E0E), (7E07, 7E15), (7E27, 7E35), (7E91, 7E9E), (8007, 8015), (8041, 804E), (8067, 8075), (8081, 808E), (8127, 8135), (8187, 8195), (8227, 8235), (8231, 823E), (8271, 827E), (8331, 833E), (8401, 840E), (8431, 843E), (8467, 8475), (84E1, 84EE), (8507, 8515), (8571, 857E), (8621, 862E), (8637, 8645), (8641, 864E), (86E1, 86EE), (8731, 873E), (8747, 8755), (8781, 878E), (8797, 87X5), (8881, 888E), (8897, 88X5), (8901, 890E), (8917, 8925), (8981, 898E), (89E7, 8X05), (8X11, 8X1E), (8X21, 8X2E), (8X47, 8X55), (8X71, 8X7E), (8X91, 8X9E), (8XX7, 8XE5), (8E37, 8E45), (8EE1, 8EEE), (9007, 9015), (9057, 9065), (9091, 909E), (9127, 9135), (9137, 9145), (9177, 9185), (9231, 923E), (9261, 926E), (9307, 9315), (9361, 936E), (9367, 9375), (9387, 9395), (9447, 9455), (9557, 9565), (95E7, 9605), (9601, 960E), (9651, 965E), (9687, 9695), (9777, 9785), (97E1, 97EE), (9927, 9935), (9961, 996E), (9967, 9975), (9X17, 9X25), (9X97, 9XX5), (X031, X03E), (X051, X05E), (X081, X08E), (X087, X095), (X137, X145), (X171, X17E), (X201, X20E), (X227, X235), (X277, X285), (X321, X32E), (X397, X3X5), (X421, X42E), (X447, X455), (X461, X46E), (X497, X4X5), (X4X1, X4XE), (X541, X54E), (X5X1, X5XE), (X5E1, X5EE), (X631, X63E), (X667, X675), (X711, X71E), (X801, X80E), (X817, X825), (X851, X85E), (X907, X915), (X971, X97E), (X997, X9X5), (XX57, XX65), (XX61, XX6E), (XXE7, XE05), (E051, E05E), (E181, E18E), (E211, E21E), (E271, E27E), (E2X1, E2XE), (E2X7, E2E5), (E307, E315), (E377, E385), (E387, E395), (E487, E495), (E497, E4X5), (E4E1, E4EE), (E521, E52E), (E597, E5X5), (E647, E655), (E677, E685), (E6E7, E705), (E777, E785), (E781, E78E), (E811, E81E), (E8X7, E8E5), (E917, E925), (E937, E945), (E947, E955), (E971, E97E), (E9X7, E9E5), (EX71, EX7E), (EE97, EEX5), ...

(p, p+10) (dozeny primes): (5, 15), (7, 17), (E, 1E), (15, 25), (17, 27), (25, 35), (27, 37), (35, 45), (3E, 4E), (4E, 5E), (51, 61), (57, 67), (5E, 6E), (75, 85), (81, 91), (85, 95), (X7, E7), (E5, 105), (E7, 107), (107, 117), (11E, 12E), (12E, 13E), (131, 141), (147, 157), (157, 167), (16E, 17E), (171, 181), (17E, 18E), (18E, 19E), (195, 1X5), (1X5, 1E5), (1X7, 1E7), (1E5, 205), (241, 251), (24E, 25E), (267, 277), (285, 295), (291, 2X1), (2X1, 2E1), (2XE, 2EE), (2E1, 301), (2EE, 30E), (315, 325), (32E, 33E), (33E, 34E), (347, 357), (34E, 35E), (365, 375), (3X5, 3E5), (40E, 41E), (421, 431), (427, 437), (437, 447), (447, 457), (455, 465), (45E, 46E), (471, 481), (507, 517), (517, 527), (531, 541), (535, 545), (565, 575), (575, 585), (577, 587), (58E, 59E), (637, 647), (655, 665), (665, 675), (68E, 69E), (6E1, 701), (701, 711), (70E, 71E), (711, 721), (727, 737), (735, 745), (737, 747), (76E, 77E), (775, 785), (791, 7X1), (7EE, 80E), (825, 835), (841, 851), (855, 865), (871, 881), (8X5, 8E5), (8X7, 8E7), (8E5, 905), (8E7, 907), (90E, 91E), (955, 965), (9XE, 9EE), (9EE, X0E), (X07, X17), (X17, X27), (X27, X37), (X35, X45), (X3E, X4E), (X4E, X5E), (X5E, X6E), (X77, X87), (X9E, XXE), (XX7, XE7), (XXE, XEE), (E11, E21), (E15, E25), (E1E, E2E), (E21, E31), (E61, E71), (E95, EX5), (EX5, EE5), (EE5, 1005), (1011, 1021), (1017, 1027), (1041, 1051), (1051, 1061), (106E, 107E), (10E1, 1101), (10E7, 1107), (1105, 1115), (1115, 1125), (1125, 1135), (1197, 11X7), (11X7, 11E7), (1201, 1211), (120E, 121E), (1245, 1255), (125E, 126E), (126E, 127E), (1295, 12X5), (1297, 12X7), (12X5, 12E5), (1367, 1377), (1391, 13X1), (13X1, 13E1), (13E5, 1405), (142E, 143E), (1457, 1467), (1461, 1471), (1465, 1475), (147E, 148E), (148E, 149E), (14EE, 150E), (156E, 157E), (1577, 1587), (15XE, 15EE), (1615, 1625), (1625, 1635), (1647, 1657), (1657, 1667), (1667, 1677), (1671, 1681), (167E, 168E), (168E, 169E), (1697, 16X7), (16X7, 16E7), (16E5, 1705), (1705, 1715), (1735, 1745), (1745, 1755), (1747, 1757), (1815, 1825), (183E, 184E), (1865, 1875), (189E, 18XE), (18XE, 18EE), (1911, 1921), (1921, 1931), (1937, 1947), (1971, 1981), (1X01, 1X11), (1X1E, 1X2E), (1X35, 1X45), (1X41, 1X51), (1X77, 1X87), (1XE1, 1E01), (1XE7, 1E07), (1E07, 1E17), (1E17, 1E27), (1E2E, 1E3E), (1E3E, 1E4E), (1E41, 1E51), (1EE5, 2005), (2001, 2011), (2037, 2047), (2051, 2061), (205E, 206E), (2061, 2071), (2077, 2087), (2087, 2097), (2097, 20X7), (20X5, 20E5), (2127, 2137), (214E, 215E), (2181, 2191), (21X7, 21E7), (221E, 222E), (2265, 2275), (228E, 229E), (22E1, 2301), (2317, 2327), (231E, 232E), (2325, 2335), (2327, 2337), (2337, 2347), (2385, 2395), (2395, 23X5), (239E, 23XE), (243E, 244E), (2457, 2467), (247E, 248E), (2535, 2545), (2537, 2547), (2545, 2555), (2547, 2557), (2555, 2565), (256E, 257E), (2571, 2581), (257E, 258E), (2607, 2617), (2615, 2625), (2665, 2675), (2675, 2685), (26XE, 26EE), (2715, 2725), (2737, 2747), (2771, 2781), (27X7, 27E7), (2825, 2835), (2827, 2837), (2837, 2847), (285E, 286E), (286E, 287E), (2895, 28X5), (292E, 293E), (2931, 2941), (2941, 2951), (29X5, 29E5), (2X1E, 2X2E), (2X2E, 2X3E), (2X51, 2X61), (2X77, 2X87), (2X87, 2X97), (2X95, 2XX5), (2X97, 2XX7), (2XEE, 2E0E), (2E3E, 2E4E), (2E51, 2E61), (2E57, 2E67), (2EX7, 2EE7), (3011, 3021), (3065, 3075), (3095, 30X5), (3145, 3155), (314E, 315E), (3167, 3177), (3177, 3187), (3187, 3197), (3191, 31X1), (31EE, 320E), (322E, 323E), (323E, 324E), (3271, 3281), (3281, 3291), (331E, 332E), (3321, 3331), (3327, 3337), (3335, 3345), (3361, 3371), (33X1, 33E1), (3417, 3427), (3435, 3445), (3457, 3467), (3467, 3477), (3475, 3485), (3481, 3491), (348E, 349E), (3491, 34X1), (351E, 352E), (3617, 3627), (3627, 3637), (3635, 3645), (3645, 3655), (3661, 3671), (366E, 367E), (3687, 3697), (3707, 3717), (3721, 3731), (3755, 3765), (377E, 378E), (378E, 379E), (379E, 37XE), (37X5, 37E5), (3821, 3831), (3827, 3837), (38E1, 3901), (395E, 396E), (3975, 3985), (39X7, 39E7), (3X31, 3X41), (3X47, 3X57), (3X55, 3X65), (3X57, 3X67), (3E0E, 3E1E), (3E11, 3E21), (3E1E, 3E2E), (3E51, 3E61), (3E75, 3E85), (3E87, 3E97), (3EXE, 3EEE), (402E, 403E), (4031, 4041), (403E, 404E), (404E, 405E), (4075, 4085), (4097, 40X7), (4101, 4111), (4145, 4155), (4207, 4217), (4281, 4291), (4291, 42X1), (42X1, 42E1), (43E1, 4401), (43EE, 440E), (4425, 4435), (4435, 4445), (4441, 4451), (444E, 445E), (4451, 4461), (4461, 4471), (4475, 4485), (4487, 4497), (4531, 4541), (4547, 4557), (454E, 455E), (4591, 45X1), (4635, 4645), (4645, 4655), (4655, 4665), (4677, 4687), (46XE, 46EE), (4715, 4725), (4727, 4737), (4805, 4815), (4815, 4825), (4821, 4831), (483E, 484E), (4887, 4897), (4897, 48X7), (4901, 4911), (490E, 491E), (4911, 4921), (491E, 492E), (4991, 49X1), (4X21, 4X31), (4X57, 4X67), (4X67, 4X77), (4E05, 4E15), (4E27, 4E37), (4E85, 4E95), (4EE1, 5001), (5025, 5035), (5031, 5041), (5035, 5045), (5057, 5067), (5067, 5077), (5085, 5095), (511E, 512E), (512E, 513E), (5145, 5155), (5155, 5165), (5201, 5211), (521E, 522E), (525E, 526E), (5261, 5271), (5285, 5295), (5317, 5327), (5375, 5385), (5397, 53X7), (53E5, 5405), (540E, 541E), (5455, 5465), (547E, 548E), (54X1, 54E1), (5527, 5537), (554E, 555E), (5551, 5561), (5585, 5595), (558E, 559E), (559E, 55XE), (5615, 5625), (562E, 563E), (5681, 5691), (5697, 56X7), (56X7, 56E7), (5701, 5711), (5725, 5735), (5761, 5771), (57X1, 57E1), (57EE, 580E), (5821, 5831), (583E, 584E), (5857, 5867), (5867, 5877), (58E5, 5905), (59XE, 59EE), (59EE, 5X0E), (5X0E, 5X1E), (5X17, 5X27), (5X4E, 5X5E), (5X5E, 5X6E), (5X75, 5X85), (5X85, 5X95), (5XXE, 5XEE), (5E1E, 5E2E), (5E2E, 5E3E), (5E55, 5E65), (5E65, 5E75), (5E81, 5E91), (5E8E, 5E9E), (5EE1, 6001), (609E, 60XE), (60E1, 6101), (6165, 6175), (6175, 6185), (6197, 61X7), (61X7, 61E7), (61E7, 6207), (6247, 6257), (633E, 634E), (6377, 6387), (63E5, 6405), (6487, 6497), (6495, 64X5), (6497, 64X7), (64X7, 64E7), (6527, 6537), (6551, 6561), (655E, 656E), (6561, 6571), (6607, 6617), (6625, 6635), (6647, 6657), (6657, 6667), (6671, 6681), (671E, 672E), (672E, 673E), (677E, 678E), (6797, 67X7), (6885, 6895), (6911, 6921), (6921, 6931), (6947, 6957), (6957, 6967), (6995, 69X5), (69X5, 69E5), (69E5, 6X05), (6X11, 6X21), (6X17, 6X27), (6X75, 6X85), (6X9E, 6XXE), (6XE1, 6E01), (6E07, 6E17), (6E15, 6E25), (6E71, 6E81), (7001, 7011), (7005, 7015), (700E, 701E), (7045, 7055), (70XE, 70EE), (70EE, 710E), (7101, 7111), (710E, 711E), (7125, 7135), (7131, 7141), (7141, 7151), (71E7, 7207), (7215, 7225), (7221, 7231), (7231, 7241), (727E, 728E), (728E, 729E), (72EE, 730E), (7311, 7321), (7341, 7351), (7351, 7361), (7361, 7371), (7395, 73X5), (739E, 73XE), (73XE, 73EE), (74E5, 7505), (7511, 7521), (7521, 7531), (756E, 757E), (7577, 7587), (757E, 758E), (75X5, 75E5), (7607, 7617), (7665, 7675), (7705, 7715), (7737, 7747), (773E, 774E), (7747, 7757), (7757, 7767), (7795, 77X5), (77X5, 77E5), (7841, 7851), (7867, 7877), (7907, 7917), (794E, 795E), (7955, 7965), (797E, 798E), (7XE1, 7E01), (7XEE, 7E0E), (7E01, 7E11), (7E15, 7E25), (7E25, 7E35), (7E27, 7E37), (7E5E, 7E6E), (8005, 8015), (8065, 8075), (8081, 8091), (8125, 8135), (8127, 8137), (8187, 8197), (8321, 8331), (83E1, 8401), (8407, 8417), (840E, 841E), (8417, 8427), (8431, 8441), (8441, 8451), (84E5, 8505), (8505, 8515), (8507, 8517), (8565, 8575), (856E, 857E), (8595, 85X5), (8645, 8655), (864E, 865E), (865E, 866E), (8667, 8677), (866E, 867E), (86EE, 870E), (872E, 873E), (873E, 874E), (878E, 879E), (87X5, 87E5), (8871, 8881), (8915, 8925), (8925, 8935), (8935, 8945), (8957, 8967), (89E7, 8X07), (8X11, 8X21), (8X1E, 8X2E), (8X37, 8X47), (8X47, 8X57), (8X71, 8X81), (8X81, 8X91), (8XE5, 8E05), (8E17, 8E27), (8E27, 8E37), (8E45, 8E55), (9015, 9025), (9047, 9057), (9065, 9075), (9081, 9091), (9097, 90X7), (909E, 90XE), (9127, 9137), (9135, 9145), (9145, 9155), (9155, 9165), (917E, 918E), (9185, 9195), (9231, 9241), (9241, 9251), (9251, 9261), (9257, 9267), (929E, 92XE), (9361, 9371), (9365, 9375), (938E, 939E), (93EE, 940E), (9475, 9485), (9565, 9575), (9581, 9591), (9605, 9615), (9655, 9665), (9701, 9711), (973E, 974E), (974E, 975E), (9775, 9785), (9785, 9795), (97XE, 97EE), (9821, 9831), (9837, 9847), (988E, 989E), (98X7, 98E7), (991E, 992E), (9935, 9945), (996E, 997E), (99E1, 9X01), (9X25, 9X35), (9X31, 9X41), (9X41, 9X51), (9E47, 9E57), (X035, X045), (X081, X091), (X091, X0X1), (X0E7, X107), (X107, X117), (X13E, X14E), (X145, X155), (X161, X171), (X197, X1X7), (X201, X211), (X225, X235), (X275, X285), (X285, X295), (X321, X331), (X331, X341), (X397, X3X7), (X3X7, X3E7), (X3E7, X407), (X42E, X43E), (X445, X455), (X447, X457), (X487, X497), (X4X1, X4E1), (X53E, X54E), (X541, X551), (X565, X575), (X59E, X5XE), (X5X1, X5E1), (X5XE, X5EE), (X621, X631), (X647, X657), (X657, X667), (X661, X671), (X695, X6X5), (X701, X711), (X711, X721), (X735, X745), (X745, X755), (X767, X777), (X795, X7X5), (X7E7, X807), (X807, X817), (X841, X851), (X891, X8X1), (X987, X997), (X9X5, X9E5), (X9EE, XX0E), (XX0E, XX1E), (XE2E, XE3E), (XE6E, XE7E), (XEE5, E005), (E051, E061), (E147, E157), (E157, E167), (E171, E181), (E1E5, E205), (E26E, E27E), (E27E, E28E), (E2X1, E2E1), (E2X5, E2E5), (E2E1, E301), (E315, E325), (E327, E337), (E331, E341), (E341, E351), (E377, E387), (E385, E395), (E39E, E3XE), (E3XE, E3EE), (E411, E421), (E487, E497), (E495, E4X5), (E4EE, E50E), (E50E, E51E), (E51E, E52E), (E561, E571), (E595, E5X5), (E655, E665), (E665, E675), (E675, E685), (E68E, E69E), (E6E7, E707), (E72E, E73E), (E761, E771), (E771, E781), (E785, E795), (E7E1, E801), (E801, E811), (E84E, E85E), (E875, E885), (E931, E941), (E937, E947), (E945, E955), (E97E, E98E), (E9X7, E9E7), (EX51, EX61), (EX61, EX71), (EX87, EX97), (EE07, EE17), (EE2E, EE3E), (EE75, EE85), (EE97, EEX7), (EEX7, EEE7), (EEE7, 10007), ...

(p, p+20) (viginty primes): (5, 25), (7, 27), (11, 31), (15, 35), (17, 37), (1E, 3E), (25, 45), (31, 51), (37, 57), (3E, 5E), (4E, 6E), (61, 81), (67, 87), (6E, 8E), (75, 95), (87, X7), (8E, XE), (95, E5), (X7, 107), (E7, 117), (105, 125), (111, 131), (11E, 13E), (125, 145), (147, 167), (16E, 18E), (175, 195), (17E, 19E), (195, 1E5), (1X5, 205), (1E7, 217), (205, 225), (217, 237), (221, 241), (251, 271), (25E, 27E), (271, 291), (291, 2E1), (2X1, 301), (2XE, 30E), (301, 321), (307, 327), (30E, 32E), (327, 347), (32E, 34E), (33E, 35E), (357, 377), (377, 397), (397, 3E7), (3XE, 40E), (3E5, 415), (401, 421), (415, 435), (427, 447), (435, 455), (437, 457), (465, 485), (46E, 48E), (485, 4X5), (4E1, 511), (4EE, 51E), (507, 527), (511, 531), (545, 565), (557, 577), (565, 585), (591, 5E1), (59E, 5EE), (5E1, 611), (5E5, 615), (5E7, 617), (5EE, 61E), (617, 637), (61E, 63E), (655, 675), (66E, 68E), (675, 695), (687, 6X7), (6E1, 711), (701, 721), (727, 747), (747, 767), (751, 771), (771, 791), (7X1, 801), (80E, 82E), (835, 855), (851, 871), (88E, 8XE), (8X5, 905), (8X7, 907), (8XE, 90E), (901, 921), (907, 927), (987, 9X7), (995, 9E5), (9X7, X07), (9XE, X0E), (9E1, X11), (X07, X27), (X17, X37), (X3E, X5E), (X4E, X6E), (X87, XX7), (X9E, XEE), (XEE, E1E), (E11, E31), (E25, E45), (E71, E91), (E95, EE5), (E97, EE7), (EX5, 1005), (EE7, 1017), (1021, 1041), (1027, 1047), (1041, 1061), (104E, 106E), (107E, 109E), (109E, 10EE), (1105, 1125), (1115, 1135), (112E, 114E), (1165, 1185), (1185, 11X5), (118E, 11XE), (1197, 11E7), (11X1, 1201), (11XE, 120E), (1211, 1231), (121E, 123E), (123E, 125E), (125E, 127E), (1261, 1281), (1281, 12X1), (1295, 12E5), (12X1, 1301), (1317, 1337), (1345, 1365), (136E, 138E), (1391, 13E1), (1395, 13E5), (13X7, 1407), (1405, 1425), (1425, 1445), (1437, 1457), (1445, 1465), (1475, 1495), (147E, 149E), (1495, 14E5), (149E, 14EE), (1601, 1621), (1615, 1635), (1635, 1655), (1647, 1667), (1657, 1677), (165E, 167E), (1677, 1697), (167E, 169E), (1681, 16X1), (1697, 16E7), (16E5, 1715), (1715, 1735), (1727, 1747), (1735, 1755), (176E, 178E), (1781, 17X1), (1785, 17X5), (17EE, 181E), (181E, 183E), (184E, 186E), (189E, 18EE), (1911, 1931), (19E7, 1X17), (19EE, 1X1E), (1X51, 1X71), (1XXE, 1E0E), (1XE7, 1E17), (1E07, 1E27), (1E0E, 1E2E), (1E2E, 1E4E), (1E65, 1E85), (1EX1, 2001), (200E, 202E), (2051, 2071), (2065, 2085), (2077, 2097), (2085, 20X5), (2087, 20X7), (20X7, 2107), (20E5, 2115), (2107, 2127), (2111, 2131), (2161, 2181), (2165, 2185), (2191, 21E1), (2221, 2241), (222E, 224E), (2245, 2265), (2267, 2287), (2291, 22E1), (2317, 2337), (2327, 2347), (232E, 234E), (2347, 2367), (2385, 23X5), (2397, 23E7), (23E7, 2417), (2415, 2435), (2481, 24X1), (2485, 24X5), (24X1, 2501), (2501, 2521), (2535, 2555), (2537, 2557), (2545, 2565), (256E, 258E), (2581, 25X1), (2617, 2637), (2625, 2645), (2645, 2665), (2665, 2685), (2687, 26X7), (26E5, 2715), (2717, 2737), (2725, 2745), (274E, 276E), (2787, 27X7), (27E1, 2811), (2827, 2847), (2835, 2855), (285E, 287E), (2907, 2927), (2931, 2951), (2935, 2955), (2X11, 2X31), (2X1E, 2X3E), (2X31, 2X51), (2X3E, 2X5E), (2X61, 2X81), (2X77, 2X97), (2X87, 2XX7), (2E31, 2E51), (2E8E, 2EXE), (3021, 3041), (3045, 3065), (3075, 3095), (307E, 309E), (30X5, 3105), (30E7, 3117), (3155, 3175), (3167, 3187), (3171, 3191), (3175, 3195), (3177, 3197), (3205, 3225), (3207, 3227), (320E, 322E), (3227, 3247), (322E, 324E), (3271, 3291), (3307, 3327), (3337, 3357), (3345, 3365), (3365, 3385), (3385, 33X5), (341E, 343E), (3457, 3477), (346E, 348E), (3481, 34X1), (349E, 34EE), (34EE, 351E), (356E, 358E), (35X5, 3605), (35E7, 3617), (3617, 3637), (3635, 3655), (36X5, 3705), (3705, 3725), (3747, 3767), (375E, 377E), (3771, 3791), (377E, 379E), (378E, 37XE), (37E5, 3815), (3801, 3821), (3807, 3827), (3831, 3851), (3851, 3871), (3877, 3897), (3895, 38E5), (3941, 3961), (3957, 3977), (3961, 3981), (3X11, 3X31), (3X47, 3X67), (3X71, 3X91), (3X95, 3XE5), (3E0E, 3E2E), (3E2E, 3E4E), (3E55, 3E75), (3E97, 3EE7), (402E, 404E), (403E, 405E), (4047, 4067), (4055, 4075), (408E, 40XE), (411E, 413E), (413E, 415E), (415E, 417E), (41XE, 420E), (4211, 4231), (4217, 4237), (4225, 4245), (426E, 428E), (4281, 42X1), (428E, 42XE), (4291, 42E1), (4321, 4341), (4341, 4361), (4375, 4395), (4395, 43E5), (440E, 442E), (4425, 4445), (442E, 444E), (4441, 4461), (4451, 4471), (445E, 447E), (447E, 449E), (4515, 4535), (4557, 4577), (455E, 457E), (4571, 4591), (4615, 4635), (4635, 4655), (4645, 4665), (4665, 4685), (4685, 46X5), (468E, 46XE), (4707, 4727), (4761, 4781), (4805, 4825), (481E, 483E), (4825, 4845), (484E, 486E), (486E, 488E), (4887, 48X7), (4901, 4921), (490E, 492E), (4947, 4967), (4951, 4971), (4955, 4975), (4967, 4987), (4971, 4991), (49X1, 4X01), (4X01, 4X21), (4X0E, 4X2E), (4X57, 4X77), (4X5E, 4X7E), (4X77, 4X97), (4E15, 4E35), (4E37, 4E57), (4E65, 4E85), (4E87, 4EX7), (4EX7, 5007), (5025, 5045), (5041, 5061), (5057, 5077), (5061, 5081), (5081, 50X1), (50E7, 5117), (50EE, 511E), (511E, 513E), (5145, 5165), (5147, 5167), (5167, 5187), (5297, 52E7), (52E7, 5317), (5327, 5347), (5331, 5351), (5347, 5367), (5351, 5371), (5355, 5375), (5371, 5391), (53XE, 540E), (5435, 5455), (5487, 54X7), (5531, 5551), (5545, 5565), (5565, 5585), (5567, 5587), (558E, 55XE), (5595, 55E5), (55E5, 5615), (5697, 56E7), (5741, 5761), (575E, 577E), (577E, 579E), (579E, 57EE), (57E7, 5817), (5835, 5855), (5857, 5877), (5877, 5897), (5897, 58E7), (5911, 5931), (5985, 59X5), (59XE, 5X0E), (59E1, 5X11), (59EE, 5X1E), (5X4E, 5X6E), (5X75, 5X95), (5XEE, 5E1E), (5E17, 5E37), (5E1E, 5E3E), (5E55, 5E75), (5E75, 5E95), (5E91, 5EE1), (6051, 6071), (6055, 6075), (6071, 6091), (607E, 609E), (6091, 60E1), (6165, 6185), (617E, 619E), (6197, 61E7), (61X7, 6207), (6207, 6227), (620E, 622E), (6227, 6247), (6245, 6265), (6261, 6281), (6331, 6351), (634E, 636E), (6357, 6377), (6405, 6425), (642E, 644E), (644E, 646E), (6487, 64X7), (6497, 64E7), (64X5, 6505), (6505, 6525), (6551, 6571), (6571, 6591), (6647, 6667), (6681, 66X1), (66E5, 6715), (671E, 673E), (673E, 675E), (6757, 6777), (675E, 677E), (6777, 6797), (67X7, 6807), (6807, 6827), (6861, 6881), (6865, 6885), (6895, 68E5), (68E5, 6915), (6911, 6931), (6947, 6967), (6995, 69E5), (699E, 69EE), (69X5, 6X05), (69EE, 6X1E), (6X27, 6X47), (6X47, 6X67), (6X7E, 6X9E), (6X85, 6XX5), (6E2E, 6E4E), (6E81, 6EX1), (6EX1, 7001), (701E, 703E), (708E, 70XE), (70XE, 710E), (70EE, 711E), (7111, 7131), (7131, 7151), (716E, 718E), (71E5, 7215), (7221, 7241), (7225, 7245), (7241, 7261), (7275, 7295), (727E, 729E), (7287, 72X7), (729E, 72EE), (72E1, 7311), (7321, 7341), (7341, 7361), (7351, 7371), (7371, 7391), (739E, 73EE), (7415, 7435), (7421, 7441), (7457, 7477), (7471, 7491), (74X7, 7507), (7511, 7531), (7565, 7585), (756E, 758E), (7585, 75X5), (75EE, 761E), (7617, 7637), (761E, 763E), (7641, 7661), (76EE, 771E), (771E, 773E), (7737, 7757), (7747, 7767), (774E, 776E), (7795, 77E5), (7817, 7837), (7855, 7875), (7905, 7925), (7921, 7941), (795E, 797E), (798E, 79XE), (79X1, 7X01), (7X15, 7X35), (7X27, 7X47), (7XE1, 7E11), (7E07, 7E27), (7E15, 7E35), (7E65, 7E85), (7EX7, 8007), (802E, 804E), (8045, 8065), (8047, 8067), (804E, 806E), (806E, 808E), (8135, 8155), (8155, 8175), (8175, 8195), (8197, 81E7), (8231, 8251), (8235, 8255), (8251, 8271), (8271, 8291), (833E, 835E), (8357, 8377), (83XE, 840E), (8407, 8427), (841E, 843E), (8431, 8451), (8467, 8487), (849E, 84EE), (84E1, 8511), (84E5, 8515), (8571, 8591), (8575, 8595), (860E, 862E), (8621, 8641), (8625, 8645), (862E, 864E), (864E, 866E), (865E, 867E), (8691, 86E1), (86E7, 8717), (870E, 872E), (872E, 874E), (8777, 8797), (8865, 8885), (8885, 88X5), (888E, 88XE), (88XE, 890E), (8915, 8935), (8925, 8945), (8961, 8981), (8981, 89X1), (89EE, 8X1E), (8X21, 8X41), (8X37, 8X57), (8X71, 8X91), (8X7E, 8X9E), (8X95, 8XE5), (8E17, 8E37), (8E2E, 8E4E), (8E55, 8E75), (8E9E, 8EEE), (9007, 9027), (9027, 9047), (9057, 9077), (9077, 9097), (907E, 909E), (9135, 9155), (9145, 9165), (915E, 917E), (9165, 9185), (9231, 9251), (9241, 9261), (9261, 9281), (9341, 9361), (9367, 9387), (936E, 938E), (9375, 9395), (9387, 93X7), (939E, 93EE), (9455, 9475), (9485, 94X5), (94X1, 9501), (9557, 9577), (960E, 962E), (9631, 9651), (9695, 96E5), (973E, 975E), (9761, 9781), (9775, 9795), (984E, 986E), (986E, 988E), (9927, 9947), (9947, 9967), (9997, 99E7), (99E7, 9X17), (9X31, 9X51), (9X51, 9X71), (9X85, 9XX5), (9X8E, 9XXE), (9E1E, 9E3E), (9E27, 9E47), (9E3E, 9E5E), (9E5E, 9E7E), (X011, X031), (X031, X051), (X03E, X05E), (X067, X087), (X081, X0X1), (X095, X0E5), (X0E7, X117), (X117, X137), (X137, X157), (X205, X225), (X227, X247), (X275, X295), (X277, X297), (X297, X2E7), (X301, X321), (X321, X341), (X35E, X37E), (X397, X3E7), (X3X7, X407), (X485, X4X5), (X4E1, X511), (X581, X5X1), (X59E, X5EE), (X647, X667), (X671, X691), (X675, X695), (X6EE, X71E), (X701, X721), (X735, X755), (X7E7, X817), (X801, X821), (X821, X841), (X851, X871), (X871, X891), (X915, X935), (X951, X971), (X9EE, XX1E), (XX25, XX45), (XX45, XX65), (E005, E025), (E0XE, E10E), (E105, E125), (E127, E147), (E147, E167), (E151, E171), (E181, E1X1), (E211, E231), (E26E, E28E), (E28E, E2XE), (E2X1, E301), (E2X7, E307), (E2E5, E315), (E307, E327), (E331, E351), (E337, E357), (E357, E377), (E395, E3E5), (E39E, E3EE), (E4EE, E51E), (E50E, E52E), (E521, E541), (E541, E561), (E577, E597), (E597, E5E7), (E5E7, E617), (E615, E635), (E635, E655), (E655, E675), (E665, E685), (E685, E6X5), (E6X5, E705), (E707, E727), (E727, E747), (E761, E781), (E78E, E7XE), (E7E1, E811), (E815, E835), (E917, E937), (E925, E945), (E955, E975), (E987, E9X7), (EX2E, EX4E), (EX51, EX71), (EE3E, EE5E), (EE85, EEX5), (EE97, EEE7), (EEX7, 10007), ...

(p, p+2, p+6) prime triplets: (5, 7, E), (E, 11, 15), (15, 17, 1E), (35, 37, 3E), (85, 87, 8E), (8E, 91, 95), (13E, 141, 145), (16E, 171, 175), (21E, 221, 225), (24E, 251, 255), (325, 327, 32E), (455, 457, 45E), (585, 587, 58E), (5E5, 5E7, 5EE), (615, 617, 61E), (76E, 771, 775), (8X5, 8X7, 8XE), (905, 907, 90E), (9XE, 9E1, 9E5), (X35, X37, X3E), (X3E, X41, X45), (E1E, E21, E25), (10EE, 1101, 1105), (11X5, 11X7, 11XE), (1255, 1257, 125E), (1365, 1367, 136E), (138E, 1391, 1395), (1655, 1657, 165E), (167E, 1681, 1685), (1X6E, 1X71, 1X75), (2005, 2007, 200E), (205E, 2061, 2065), (215E, 2161, 2165), (2325, 2327, 232E), (2395, 2397, 239E), (247E, 2481, 2485), (2745, 2747, 274E), (2825, 2827, 282E), (292E, 2931, 2935), (2X2E, 2X31, 2X35), (2X5E, 2X61, 2X65), (303E, 3041, 3045), (3205, 3207, 320E), (3225, 3227, 322E), (332E, 3331, 3335), (3705, 3707, 370E), (3E4E, 3E51, 3E55), (4685, 4687, 468E), (481E, 4821, 4825), (491E, 4921, 4925), (496E, 4971, 4975), (4E35, 4E37, 4E3E), (5165, 5167, 516E), (555E, 5561, 5565), (5585, 5587, 558E), (5E8E, 5E91, 5E95), (604E, 6051, 6055), (6075, 6077, 607E), (656E, 6571, 6575), (6995, 6997, 699E), (700E, 7011, 7015), (7585, 7587, 758E), (7635, 7637, 763E), (7E0E, 7E11, 7E15), (7E65, 7E67, 7E6E), (8045, 8047, 804E), (8065, 8067, 806E), (8195, 8197, 819E), (8355, 8357, 835E), (856E, 8571, 8575), (9075, 9077, 907E), (912E, 9131, 9135), (9365, 9367, 936E), (936E, 9371, 9375), (944E, 9451, 9455), (9X2E, 9X31, 9X35), (X08E, X091, X095), (X535, X537, X53E), (X68E, X691, X695), (XE3E, XE41, XE45), (E2X5, E2X7, E2XE), (E2XE, E2E1, E2E5), (E69E, E6X1, E6X5), (EX25, EX27, EX2E), ...

(p, p+4, p+6) prime triplets: (7, E, 11), (11, 15, 17), (31, 35, 37), (57, 5E, 61), (81, 85, 87), (87, 8E, 91), (141, 145, 147), (167, 16E, 171), (1E1, 1E5, 1E7), (217, 21E, 221), (321, 325, 327), (431, 435, 437), (587, 58E, 591), (5E1, 5E5, 5E7), (611, 615, 617), (767, 76E, 771), (901, 905, 907), (9X7, 9XE, 9E1), (X07, X0E, X11), (X37, X3E, X41), (E67, E6E, E71), (E91, E95, E97), (1047, 104E, 1051), (10E7, 10EE, 1101), (1101, 1105, 1107), (11X1, 11X5, 11X7), (1257, 125E, 1261), (12X1, 12X5, 12X7), (1461, 1465, 1467), (1677, 167E, 1681), (1697, 169E, 16X1), (1751, 1755, 1757), (19E7, 19EE, 1X01), (1X71, 1X75, 1X77), (2001, 2005, 2007), (2007, 200E, 2011), (2287, 228E, 2291), (24X1, 24X5, 24X7), (2741, 2745, 2747), (2927, 292E, 2931), (3037, 303E, 3041), (3171, 3175, 3177), (3191, 3195, 3197), (3327, 332E, 3331), (3331, 3335, 3337), (33X1, 33X5, 33X7), (3957, 395E, 3961), (3E47, 3E4E, 3E51), (4207, 420E, 4211), (45X1, 45X5, 45X7), (4681, 4685, 4687), (4967, 496E, 4971), (4EX7, 4EXE, 4EE1), (5267, 526E, 5271), (5451, 5455, 5457), (54X1, 54X5, 54X7), (5561, 5565, 5567), (5E37, 5E3E, 5E41), (6071, 6075, 6077), (6521, 6525, 6527), (6X17, 6X1E, 6X21), (6E71, 6E75, 6E77), (7051, 7055, 7057), (71E1, 71E5, 71E7), (7637, 763E, 7641), (7E07, 7E0E, 7E11), (8041, 8045, 8047), (8511, 8515, 8517), (9077, 907E, 9081), (9127, 912E, 9131), (9131, 9135, 9137), (9361, 9365, 9367), (9367, 936E, 9371), (9447, 944E, 9451), (9627, 962E, 9631), (9E57, 9E5E, 9E61), (X087, X08E, X091), (X537, X53E, X541), (X5X7, X5XE, X5E1), (X717, X71E, X721), (X871, X875, X877), (XE41, XE45, XE47), (E147, E14E, E151), (E2X1, E2X5, E2X7), (E2X7, E2XE, E2E1), (E7X7, E7XE, E7E1), (E941, E945, E947), ...

(p, p+6, p+10) (sexy prime triplets): (5, E, 15), (7, 11, 17), (E, 15, 1E), (15, 1E, 25), (27, 31, 37), (35, 3E, 45), (3E, 45, 4E), (51, 57, 61), (57, 61, 67), (81, 87, 91), (85, 8E, 95), (107, 111, 117), (11E, 125, 12E), (16E, 175, 17E), (18E, 195, 19E), (195, 19E, 1X5), (1X7, 1E1, 1E7), (24E, 255, 25E), (267, 271, 277), (3X5, 3XE, 3E5), (40E, 415, 41E), (421, 427, 431), (427, 431, 437), (455, 45E, 465), (45E, 465, 46E), (507, 511, 517), (665, 66E, 675), (68E, 695, 69E), (76E, 775, 77E), (775, 77E, 785), (791, 797, 7X1), (825, 82E, 835), (855, 85E, 865), (8X5, 8XE, 8E5), (8E7, 901, 907), (955, 95E, 965), (9XE, 9E5, 9EE), (X07, X11, X17), (X35, X3E, X45), (X3E, X45, X4E), (E15, E1E, E25), (E1E, E25, E2E), (E61, E67, E71), (1011, 1017, 1021), (1017, 1021, 1027), (1041, 1047, 1051), (10E1, 10E7, 1101), (10E7, 1101, 1107), (1125, 112E, 1135), (1197, 11X1, 11X7), (1297, 12X1, 12X7), (13X1, 13X7, 13E1), (1457, 1461, 1467), (1461, 1467, 1471), (148E, 1495, 149E), (1667, 1671, 1677), (1671, 1677, 1681), (167E, 1685, 168E), (1697, 16X1, 16X7), (1747, 1751, 1757), (1815, 181E, 1825), (1865, 186E, 1875), (1XE1, 1XE7, 1E01), (1XE7, 1E01, 1E07), (2001, 2007, 2011), (205E, 2065, 206E), (2127, 2131, 2137), (21X7, 21E1, 21E7), (231E, 2325, 232E), (2325, 232E, 2335), (2395, 239E, 23X5), (239E, 23X5, 23XE), (247E, 2485, 248E), (26XE, 26E5, 26EE), (2737, 2741, 2747), (27X7, 27E1, 27E7), (2825, 282E, 2835), (2837, 2841, 2847), (292E, 2935, 293E), (2X2E, 2X35, 2X3E), (2X77, 2X81, 2X87), (2E51, 2E57, 2E61), (2E57, 2E61, 2E67), (3095, 309E, 30X5), (3145, 314E, 3155), (314E, 3155, 315E), (3167, 3171, 3177), (3187, 3191, 3197), (3191, 3197, 31X1), (31EE, 3205, 320E), (3271, 3277, 3281), (3321, 3327, 3331), (3327, 3331, 3337), (33X1, 33X7, 33E1), (3435, 343E, 3445), (3617, 3621, 3627), (3755, 375E, 3765), (379E, 37X5, 37XE), (37X5, 37XE, 37E5), (3821, 3827, 3831), (3827, 3831, 3837), (3E75, 3E7E, 3E85), (404E, 4055, 405E), (4207, 4211, 4217), (4425, 442E, 4435), (4475, 447E, 4485), (4635, 463E, 4645), (4677, 4681, 4687), (4815, 481E, 4825), (483E, 4845, 484E), (491E, 4925, 492E), (5057, 5061, 5067), (5085, 508E, 5095), (5261, 5267, 5271), (54X1, 54X7, 54E1), (5527, 5531, 5537), (5585, 558E, 5595), (558E, 5595, 559E), (5E1E, 5E25, 5E2E), (5E8E, 5E95, 5E9E), (6175, 617E, 6185), (61E7, 6201, 6207), (633E, 6345, 634E), (6797, 67X1, 67X7), (6995, 699E, 69X5), (69E5, 69EE, 6X05), (6X11, 6X17, 6X21), (6X17, 6X21, 6X27), (6X75, 6X7E, 6X85), (6X9E, 6XX5, 6XXE), (6E71, 6E77, 6E81), (7005, 700E, 7015), (700E, 7015, 701E), (728E, 7295, 729E), (7311, 7317, 7321), (7341, 7347, 7351), (7395, 739E, 73X5), (739E, 73X5, 73XE), (757E, 7585, 758E), (7607, 7611, 7617), (7665, 766E, 7675), (7757, 7761, 7767), (794E, 7955, 795E), (7955, 795E, 7965), (7E01, 7E07, 7E11), (7E5E, 7E65, 7E6E), (8065, 806E, 8075), (84E5, 84EE, 8505), (8507, 8511, 8517), (8565, 856E, 8575), (856E, 8575, 857E), (8645, 864E, 8655), (864E, 8655, 865E), (8957, 8961, 8967), (8X37, 8X41, 8X47), (8E45, 8E4E, 8E55), (9127, 9131, 9137), (9155, 915E, 9165), (917E, 9185, 918E), (9185, 918E, 9195), (9251, 9257, 9261), (9257, 9261, 9267), (9361, 9367, 9371), (9365, 936E, 9375), (938E, 9395, 939E), (9475, 947E, 9485), (9605, 960E, 9615), (9655, 965E, 9665), (9701, 9707, 9711), (996E, 9975, 997E), (99E1, 99E7, 9X01), (9X25, 9X2E, 9X35), (9X41, 9X47, 9X51), (X035, X03E, X045), (X081, X087, X091), (X13E, X145, X14E), (X145, X14E, X155), (X5X1, X5X7, X5E1), (X657, X661, X667), (X661, X667, X671), (X711, X717, X721), (X7E7, X801, X807), (E147, E151, E157), (E2X1, E2X7, E2E1), (E2X5, E2XE, E2E5), (E315, E31E, E325), (E327, E331, E337), (E331, E337, E341), (E3XE, E3E5, E3EE), (E411, E417, E421), (E771, E777, E781), (E785, E78E, E795), (E931, E937, E941), (E937, E941, E947), ...

(p, p+10, p+20) (dozeny prime triplets): (5, 15, 25), (7, 17, 27), (15, 25, 35), (17, 27, 37), (25, 35, 45), (3E, 4E, 5E), (4E, 5E, 6E), (75, 85, 95), (X7, E7, 107), (E7, 107, 117), (11E, 12E, 13E), (147, 157, 167), (16E, 17E, 18E), (17E, 18E, 19E), (195, 1X5, 1E5), (1X5, 1E5, 205), (291, 2X1, 2E1), (2X1, 2E1, 301), (2XE, 2EE, 30E), (32E, 33E, 34E), (33E, 34E, 35E), (427, 437, 447), (437, 447, 457), (507, 517, 527), (565, 575, 585), (655, 665, 675), (6E1, 701, 711), (701, 711, 721), (727, 737, 747), (8X5, 8E5, 905), (8X7, 8E7, 907), (9XE, 9EE, X0E), (X07, X17, X27), (X17, X27, X37), (X3E, X4E, X5E), (X4E, X5E, X6E), (X9E, XXE, XEE), (E11, E21, E31), (E95, EX5, EE5), (EX5, EE5, 1005), (1041, 1051, 1061), (1105, 1115, 1125), (1115, 1125, 1135), (1197, 11X7, 11E7), (125E, 126E, 127E), (1295, 12X5, 12E5), (1391, 13X1, 13E1), (147E, 148E, 149E), (1615, 1625, 1635), (1647, 1657, 1667), (1657, 1667, 1677), (167E, 168E, 169E), (1697, 16X7, 16E7), (16E5, 1705, 1715), (1735, 1745, 1755), (189E, 18XE, 18EE), (1911, 1921, 1931), (1XE7, 1E07, 1E17), (1E07, 1E17, 1E27), (1E2E, 1E3E, 1E4E), (2051, 2061, 2071), (2077, 2087, 2097), (2087, 2097, 20X7), (2317, 2327, 2337), (2327, 2337, 2347), (2385, 2395, 23X5), (2535, 2545, 2555), (2537, 2547, 2557), (2545, 2555, 2565), (256E, 257E, 258E), (2665, 2675, 2685), (2827, 2837, 2847), (285E, 286E, 287E), (2931, 2941, 2951), (2X1E, 2X2E, 2X3E), (2X77, 2X87, 2X97), (2X87, 2X97, 2XX7), (3167, 3177, 3187), (3177, 3187, 3197), (322E, 323E, 324E), (3271, 3281, 3291), (3457, 3467, 3477), (3481, 3491, 34X1), (3617, 3627, 3637), (3635, 3645, 3655), (377E, 378E, 379E), (378E, 379E, 37XE), (3X47, 3X57, 3X67), (3E0E, 3E1E, 3E2E), (402E, 403E, 404E), (403E, 404E, 405E), (4281, 4291, 42X1), (4291, 42X1, 42E1), (4425, 4435, 4445), (4441, 4451, 4461), (4451, 4461, 4471), (4635, 4645, 4655), (4645, 4655, 4665), (4805, 4815, 4825), (4887, 4897, 48X7), (4901, 4911, 4921), (490E, 491E, 492E), (4X57, 4X67, 4X77), (5025, 5035, 5045), (5057, 5067, 5077), (511E, 512E, 513E), (5145, 5155, 5165), (558E, 559E, 55XE), (5697, 56X7, 56E7), (5857, 5867, 5877), (59XE, 59EE, 5X0E), (59EE, 5X0E, 5X1E), (5X4E, 5X5E, 5X6E), (5X75, 5X85, 5X95), (5E1E, 5E2E, 5E3E), (5E55, 5E65, 5E75), (6165, 6175, 6185), (6197, 61X7, 61E7), (61X7, 61E7, 6207), (6487, 6497, 64X7), (6497, 64X7, 64E7), (6551, 6561, 6571), (6647, 6657, 6667), (671E, 672E, 673E), (6911, 6921, 6931), (6947, 6957, 6967), (6995, 69X5, 69E5), (69X5, 69E5, 6X05), (70XE, 70EE, 710E), (70EE, 710E, 711E), (7131, 7141, 7151), (7221, 7231, 7241), (727E, 728E, 729E), (7341, 7351, 7361), (7351, 7361, 7371), (739E, 73XE, 73EE), (7511, 7521, 7531), (756E, 757E, 758E), (7737, 7747, 7757), (7747, 7757, 7767), (7795, 77X5, 77E5), (7XE1, 7E01, 7E11), (7E15, 7E25, 7E35), (8407, 8417, 8427), (8431, 8441, 8451), (84E5, 8505, 8515), (864E, 865E, 866E), (865E, 866E, 867E), (872E, 873E, 874E), (8915, 8925, 8935), (8925, 8935, 8945), (8X37, 8X47, 8X57), (8X71, 8X81, 8X91), (8E17, 8E27, 8E37), (9135, 9145, 9155), (9145, 9155, 9165), (9231, 9241, 9251), (9241, 9251, 9261), (973E, 974E, 975E), (9775, 9785, 9795), (9X31, 9X41, 9X51), (X081, X091, X0X1), (X0E7, X107, X117), (X275, X285, X295), (X321, X331, X341), (X397, X3X7, X3E7), (X3X7, X3E7, X407), (X59E, X5XE, X5EE), (X647, X657, X667), (X701, X711, X721), (X735, X745, X755), (X7E7, X807, X817), (X9EE, XX0E, XX1E), (E147, E157, E167), (E26E, E27E, E28E), (E2X1, E2E1, E301), (E331, E341, E351), (E39E, E3XE, E3EE), (E4EE, E50E, E51E), (E50E, E51E, E52E), (E655, E665, E675), (E665, E675, E685), (E761, E771, E781), (E7E1, E801, E811), (EX51, EX61, EX71), (EE97, EEX7, EEE7), (EEX7, EEE7, 10007), ...

(p, p+2, p+6, p+8) prime quadruplets: (5, 7, E, 11), (E, 11, 15, 17), (85, 87, 8E, 91), (13E, 141, 145, 147), (585, 587, 58E, 591), (X35, X37, X3E, X41), (10EE, 1101, 1105, 1107), (1255, 1257, 125E, 1261), (1X6E, 1X71, 1X75, 1X77), (2005, 2007, 200E, 2011), (332E, 3331, 3335, 3337), (555E, 5561, 5565, 5567), (7635, 7637, 763E, 7641), (9075, 9077, 907E, 9081), (912E, 9131, 9135, 9137), (9365, 9367, 936E, 9371), (X535, X537, X53E, X541), (XE3E, XE41, XE45, XE47), (E2X5, E2X7, E2XE, E2E1), (101XE, 101E1, 101E5, 101E7), (10X7E, 10X81, 10X85, 10X87), (12785, 12787, 1278E, 12791), (16435, 16437, 1643E, 16441), (181E5, 181E7, 181EE, 18201), (21405, 21407, 2140E, 21411), (25865, 25867, 2586E, 25871), (2802E, 28031, 28035, 28037), (30545, 30547, 3054E, 30551), (32X8E, 32X91, 32X95, 32X97), (3426E, 34271, 34275, 34277), (35965, 35967, 3596E, 35971), (38865, 38867, 3886E, 38871), (3X14E, 3X151, 3X155, 3X157), (3XX95, 3XX97, 3XX9E, 3XXX1), (3EX55, 3EX57, 3EX5E, 3EX61), (4348E, 43491, 43495, 43497), (48755, 48757, 4875E, 48761), (4944E, 49451, 49455, 49457), (4X61E, 4X621, 4X625, 4X627), (53695, 53697, 5369E, 536X1), (5752E, 57531, 57535, 57537), (5904E, 59051, 59055, 59057), (5X875, 5X877, 5X87E, 5X881), (66485, 66487, 6648E, 66491), (6E515, 6E517, 6E51E, 6E521), (7701E, 77021, 77025, 77027), (7EX85, 7EX87, 7EX8E, 7EX91), (80675, 80677, 8067E, 80681), (83075, 83077, 8307E, 83081), (906EE, 90701, 90705, 90707), (94925, 94927, 9492E, 94931), (9532E, 95331, 95335, 95337), (9872E, 98731, 98735, 98737), (98965, 98967, 9896E, 98971), (X5955, X5957, X595E, X5961), (XX4X5, XX4X7, XX4XE, XX4E1), (E6XE5, E6XE7, E6XEE, E6E01), (E9045, E9047, E904E, E9051), (EE355, EE357, EE35E, EE361), (EE61E, EE621, EE625, EE627), ...

(p, p+4, p+6, p+X) prime quadruplets: (7, E, 11, 15), (11, 15, 17, 1E), (31, 35, 37, 3E), (81, 85, 87, 8E), (87, 8E, 91, 95), (167, 16E, 171, 175), (217, 21E, 221, 225), (321, 325, 327, 32E), (5E1, 5E5, 5E7, 5EE), (611, 615, 617, 61E), (767, 76E, 771, 775), (901, 905, 907, 90E), (9X7, 9XE, 9E1, 9E5), (X37, X3E, X41, X45), (10E7, 10EE, 1101, 1105), (11X1, 11X5, 11X7, 11XE), (1677, 167E, 1681, 1685), (2001, 2005, 2007, 200E), (2741, 2745, 2747, 274E), (2927, 292E, 2931, 2935), (3037, 303E, 3041, 3045), (3327, 332E, 3331, 3335), (3E47, 3E4E, 3E51, 3E55), (4681, 4685, 4687, 468E), (4967, 496E, 4971, 4975), (6071, 6075, 6077, 607E), (7E07, 7E0E, 7E11, 7E15), (8041, 8045, 8047, 804E), (9127, 912E, 9131, 9135), (9361, 9365, 9367, 936E), (9367, 936E, 9371, 9375), (9447, 944E, 9451, 9455), (X087, X08E, X091, X095), (E2X1, E2X5, E2X7, E2XE), (E2X7, E2XE, E2E1, E2E5), (10007, 1000E, 10011, 10015), (101E1, 101E5, 101E7, 101EE), (10401, 10405, 10407, 1040E), (10X81, 10X85, 10X87, 10X8E), (11411, 11415, 11417, 1141E), (11771, 11775, 11777, 1177E), (11807, 1180E, 11811, 11815), (11E47, 11E4E, 11E51, 11E55), (14071, 14075, 14077, 1407E), (14961, 14965, 14967, 1496E), (161E7, 161EE, 16201, 16205), (17367, 1736E, 17371, 17375), (17551, 17555, 17557, 1755E), (18687, 1868E, 18691, 18695), (18X07, 18X0E, 18X11, 18X15), (19E97, 19E9E, 19EX1, 19EX5), (1E487, 1E48E, 1E491, 1E495), (20391, 20395, 20397, 2039E), (206X1, 206X5, 206X7, 206XE), (21401, 21405, 21407, 2140E), (21407, 2140E, 21411, 21415), (21747, 2174E, 21751, 21755), (22621, 22625, 22627, 2262E), (25761, 25765, 25767, 2576E), (27651, 27655, 27657, 2765E), (28031, 28035, 28037, 2803E), (28371, 28375, 28377, 2837E), (2E301, 2E305, 2E307, 2E30E), (3X147, 3X14E, 3X151, 3X155), (3X831, 3X835, 3X837, 3X83E), (3XX71, 3XX75, 3XX77, 3XX7E), (3E557, 3E55E, 3E561, 3E565), (41E27, 41E2E, 41E31, 41E35), (43381, 43385, 43387, 4338E), (43487, 4348E, 43491, 43495), (44391, 44395, 44397, 4439E), (44477, 4447E, 44481, 44485), (44E11, 44E15, 44E17, 44E1E), (45561, 45565, 45567, 4556E), (458X1, 458X5, 458X7, 458XE), (46127, 4612E, 46131, 46135), (46181, 46185, 46187, 4618E), (47037, 4703E, 47041, 47045), (48171, 48175, 48177, 4817E), (48X91, 48X95, 48X97, 48X9E), (4X617, 4X61E, 4X621, 4X625), (4X907, 4X90E, 4X911, 4X915), (53011, 53015, 53017, 5301E), (53E97, 53E9E, 53EX1, 53EX5), (54231, 54235, 54237, 5423E), (54627, 5462E, 54631, 54635), (554X1, 554X5, 554X7, 554XE), (55587, 5558E, 55591, 55595), (555X7, 555XE, 555E1, 555E5), (56101, 56105, 56107, 5610E), (57081, 57085, 57087, 5708E), (577E7, 577EE, 57801, 57805), (58981, 58985, 58987, 5898E), (59EX1, 59EX5, 59EX7, 59EXE), (5E727, 5E72E, 5E731, 5E735), (61067, 6106E, 61071, 61075), (64837, 6483E, 64841, 64845), (65X77, 65X7E, 65X81, 65X85), (66E21, 66E25, 66E27, 66E2E), (6E517, 6E51E, 6E521, 6E525), (71897, 7189E, 718X1, 718X5), (73031, 73035, 73037, 7303E), (73631, 73635, 73637, 7363E), (74541, 74545, 74547, 7454E), (746E7, 746EE, 74701, 74705), (75E01, 75E05, 75E07, 75E0E), (7X731, 7X735, 7X737, 7X73E), (7XX97, 7XX9E, 7XXX1, 7XXX5), (7E321, 7E325, 7E327, 7E32E), (7EX87, 7EX8E, 7EX91, 7EX95), (80677, 8067E, 80681, 80685), (82E97, 82E9E, 82EX1, 82EX5), (837E1, 837E5, 837E7, 837EE), (84691, 84695, 84697, 8469E), (86E37, 86E3E, 86E41, 86E45), (88177, 8817E, 88181, 88185), (90357, 9035E, 90361, 90365), (92351, 92355, 92357, 9235E), (93017, 9301E, 93021, 93025), (94051, 94055, 94057, 9405E), (94X57, 94X5E, 94X61, 94X65), (95331, 95335, 95337, 9533E), (954X7, 954XE, 954E1, 954E5), (97087, 9708E, 97091, 97095), (98967, 9896E, 98971, 98975), (993E7, 993EE, 99401, 99405), (99X31, 99X35, 99X37, 99X3E), (9XX61, 9XX65, 9XX67, 9XX6E), (X3987, X398E, X3991, X3995), (X6251, X6255, X6257, X625E), (X7211, X7215, X7217, X721E), (X7X01, X7X05, X7X07, X7X0E), (X8381, X8385, X8387, X838E), (XX371, XX375, XX377, XX37E), (XX401, XX405, XX407, XX40E), (XX4X7, XX4XE, XX4E1, XX4E5), (XE311, XE315, XE317, XE31E), (E13X7, E13XE, E13E1, E13E5), (E3297, E329E, E32X1, E32X5), (E3637, E363E, E3641, E3645), (E3821, E3825, E3827, E382E), (E3EE7, E3EEE, E4001, E4005), (E4547, E454E, E4551, E4555), (E5867, E586E, E5871, E5875), (EE357, EE35E, EE361, EE365), ...

(p, p+6, p+10, p+16) (sexy prime quadruplets): (5, E, 15, 1E), (E, 15, 1E, 25), (35, 3E, 45, 4E), (51, 57, 61, 67), (18E, 195, 19E, 1X5), (421, 427, 431, 437), (455, 45E, 465, 46E), (76E, 775, 77E, 785), (X35, X3E, X45, X4E), (E15, E1E, E25, E2E), (1011, 1017, 1021, 1027), (10E1, 10E7, 1101, 1107), (1457, 1461, 1467, 1471), (1667, 1671, 1677, 1681), (1XE1, 1XE7, 1E01, 1E07), (231E, 2325, 232E, 2335), (2395, 239E, 23X5, 23XE), (2E51, 2E57, 2E61, 2E67), (3145, 314E, 3155, 315E), (3187, 3191, 3197, 31X1), (3321, 3327, 3331, 3337), (379E, 37X5, 37XE, 37E5), (3821, 3827, 3831, 3837), (5585, 558E, 5595, 559E), (6X11, 6X17, 6X21, 6X27), (7005, 700E, 7015, 701E), (7395, 739E, 73X5, 73XE), (794E, 7955, 795E, 7965), (8565, 856E, 8575, 857E), (8645, 864E, 8655, 865E), (917E, 9185, 918E, 9195), (9251, 9257, 9261, 9267), (X13E, X145, X14E, X155), (X657, X661, X667, X671), (E327, E331, E337, E341), (E931, E937, E941, E947), (10521, 10527, 10531, 10537), (115E5, 115EE, 11605, 1160E), (11E37, 11E41, 11E47, 11E51), (1318E, 13195, 1319E, 131X5), (13535, 1353E, 13545, 1354E), (1355E, 13565, 1356E, 13575), (154E7, 15501, 15507, 15511), (15887, 15891, 15897, 158X1), (1666E, 16675, 1667E, 16685), (198X1, 198X7, 198E1, 198E7), (20331, 20337, 20341, 20347), (20647, 20651, 20657, 20661), (2192E, 21935, 2193E, 21945), (25331, 25337, 25341, 25347), (27037, 27041, 27047, 27051), (27E41, 27E47, 27E51, 27E57), (28555, 2855E, 28565, 2856E), (2EEE5, 2EEEE, 30005, 3000E), (30X37, 30X41, 30X47, 30X51), (32031, 32037, 32041, 32047), (33X4E, 33X55, 33X5E, 33X65), (34607, 34611, 34617, 34621), (35351, 35357, 35361, 35367), (37855, 3785E, 37865, 3786E), (38X67, 38X71, 38X77, 38X81), (3971E, 39725, 3972E, 39735), (3X22E, 3X235, 3X23E, 3X245), (3X9X7, 3X9E1, 3X9E7, 3XX01), (3EXX5, 3EXXE, 3EXE5, 3EXEE), (40347, 40351, 40357, 40361), (40X3E, 40X45, 40X4E, 40X55), (427E1, 427E7, 42801, 42807), (43481, 43487, 43491, 43497), (43691, 43697, 436X1, 436X7), (43885, 4388E, 43895, 4389E), (449E7, 44X01, 44X07, 44X11), (46785, 4678E, 46795, 4679E), (47165, 4716E, 47175, 4717E), (47607, 47611, 47617, 47621), (5021E, 50225, 5022E, 50235), (5071E, 50725, 5072E, 50735), (50E81, 50E87, 50E91, 50E97), (51141, 51147, 51151, 51157), (52X47, 52X51, 52X57, 52X61), (54235, 5423E, 54245, 5424E), (5518E, 55195, 5519E, 551X5), (56E9E, 56EX5, 56EXE, 56EE5), (59227, 59231, 59237, 59241), (5991E, 59925, 5992E, 59935), (59XE7, 59E01, 59E07, 59E11), (5X035, 5X03E, 5X045, 5X04E), (5X745, 5X74E, 5X755, 5X75E), (5EE17, 5EE21, 5EE27, 5EE31), (60491, 60497, 604X1, 604X7), (61241, 61247, 61251, 61257), (63761, 63767, 63771, 63777), (68737, 68741, 68747, 68751), (69771, 69777, 69781, 69787), (6E581, 6E587, 6E591, 6E597), (74611, 74617, 74621, 74627), (751X5, 751XE, 751E5, 751EE), (79X8E, 79X95, 79X9E, 79XX5), (7X995, 7X99E, 7X9X5, 7X9XE), (7EX85, 7EX8E, 7EX95, 7EX9E), (83945, 8394E, 83955, 8395E), (84131, 84137, 84141, 84147), (88075, 8807E, 88085, 8808E), (8E10E, 8E115, 8E11E, 8E125), (90187, 90191, 90197, 901X1), (90515, 9051E, 90525, 9052E), (92665, 9266E, 92675, 9267E), (92955, 9295E, 92965, 9296E), (97077, 97081, 97087, 97091), (9E285, 9E28E, 9E295, 9E29E), (9E3X7, 9E3E1, 9E3E7, 9E401), (X412E, X4135, X413E, X4145), (X6297, X62X1, X62X7, X62E1), (X879E, X87X5, X87XE, X87E5), (X9235, X923E, X9245, X924E), (X9647, X9651, X9657, X9661), (XE19E, XE1X5, XE1XE, XE1E5), (E0521, E0527, E0531, E0537), (E1291, E1297, E12X1, E12X7), (E1661, E1667, E1671, E1677), (E8E15, E8E1E, E8E25, E8E2E), (EX265, EX26E, EX275, EX27E), ...

(p, p+10, p+20, p+30) (dozeny prime quadruplets): (5, 15, 25, 35), (7, 17, 27, 37), (15, 25, 35, 45), (3E, 4E, 5E, 6E), (X7, E7, 107, 117), (16E, 17E, 18E, 19E), (195, 1X5, 1E5, 205), (291, 2X1, 2E1, 301), (32E, 33E, 34E, 35E), (427, 437, 447, 457), (6E1, 701, 711, 721), (X07, X17, X27, X37), (X3E, X4E, X5E, X6E), (E95, EX5, EE5, 1005), (1105, 1115, 1125, 1135), (1647, 1657, 1667, 1677), (1XE7, 1E07, 1E17, 1E27), (2077, 2087, 2097, 20X7), (2317, 2327, 2337, 2347), (2535, 2545, 2555, 2565), (2X77, 2X87, 2X97, 2XX7), (3167, 3177, 3187, 3197), (377E, 378E, 379E, 37XE), (402E, 403E, 404E, 405E), (4281, 4291, 42X1, 42E1), (4441, 4451, 4461, 4471), (4635, 4645, 4655, 4665), (59XE, 59EE, 5X0E, 5X1E), (6197, 61X7, 61E7, 6207), (6487, 6497, 64X7, 64E7), (6995, 69X5, 69E5, 6X05), (70XE, 70EE, 710E, 711E), (7341, 7351, 7361, 7371), (7737, 7747, 7757, 7767), (864E, 865E, 866E, 867E), (8915, 8925, 8935, 8945), (9135, 9145, 9155, 9165), (9231, 9241, 9251, 9261), (X397, X3X7, X3E7, X407), (E4EE, E50E, E51E, E52E), (E655, E665, E675, E685), (EE97, EEX7, EEE7, 10007), (105X1, 105E1, 10601, 10611), (108E7, 10907, 10917, 10927), (10X5E, 10X6E, 10X7E, 10X8E), (113X1, 113E1, 11401, 11411), (11E41, 11E51, 11E61, 11E71), (13081, 13091, 130X1, 130E1), (1353E, 1354E, 1355E, 1356E), (1409E, 140XE, 140EE, 1410E), (14307, 14317, 14327, 14337), (1467E, 1468E, 1469E, 146XE), (1500E, 1501E, 1502E, 1503E), (15X01, 15X11, 15X21, 15X31), (16957, 16967, 16977, 16987), (17521, 17531, 17541, 17551), (17917, 17927, 17937, 17947), (183X5, 183E5, 18405, 18415), (19881, 19891, 198X1, 198E1), (1E247, 1E257, 1E267, 1E277), (1E537, 1E547, 1E557, 1E567), (1E9E5, 1EX05, 1EX15, 1EX25), (20491, 204X1, 204E1, 20501), (21581, 21591, 215X1, 215E1), (21741, 21751, 21761, 21771), (2190E, 2191E, 2192E, 2193E), (24327, 24337, 24347, 24357), (25925, 25935, 25945, 25955), (26485, 26495, 264X5, 264E5), (265E5, 26605, 26615, 26625), (26871, 26881, 26891, 268X1), (2906E, 2907E, 2908E, 2909E), (2993E, 2994E, 2995E, 2996E), (2X311, 2X321, 2X331, 2X341), (2EX3E, 2EX4E, 2EX5E, 2EX6E), (35331, 35341, 35351, 35361), (37915, 37925, 37935, 37945), (37E67, 37E77, 37E87, 37E97), (38E5E, 38E6E, 38E7E, 38E8E), (3929E, 392XE, 392EE, 3930E), (3E375, 3E385, 3E395, 3E3X5), (4019E, 401XE, 401EE, 4020E), (43E71, 43E81, 43E91, 43EX1), (4489E, 448XE, 448EE, 4490E), (45691, 456X1, 456E1, 45701), (45755, 45765, 45775, 45785), (4875E, 4876E, 4877E, 4878E), (4X3XE, 4X3EE, 4X40E, 4X41E), (4X885, 4X895, 4X8X5, 4X8E5), (4E1X1, 4E1E1, 4E201, 4E211), (501EE, 5020E, 5021E, 5022E), (50225, 50235, 50245, 50255), (50X8E, 50X9E, 50XXE, 50XEE), (51881, 51891, 518X1, 518E1), (52971, 52981, 52991, 529X1), (53667, 53677, 53687, 53697), (54635, 54645, 54655, 54665), (554XE, 554EE, 5550E, 5551E), (56EX5, 56EE5, 57005, 57015), (57051, 57061, 57071, 57081), (58617, 58627, 58637, 58647), (5936E, 5937E, 5938E, 5939E), (59597, 595X7, 595E7, 59607), (6055E, 6056E, 6057E, 6058E), (623E1, 62401, 62411, 62421), (6E045, 6E055, 6E065, 6E075), (73841, 73851, 73861, 73871), (749X7, 749E7, 74X07, 74X17), (75337, 75347, 75357, 75367), (76031, 76041, 76051, 76061), (761E1, 76201, 76211, 76221), (764X1, 764E1, 76501, 76511), (76E87, 76E97, 76EX7, 76EE7), (78E57, 78E67, 78E77, 78E87), (79705, 79715, 79725, 79735), (7X99E, 7X9XE, 7X9EE, 7XX0E), (83311, 83321, 83331, 83341), (83395, 833X5, 833E5, 83405), (845X7, 845E7, 84607, 84617), (85155, 85165, 85175, 85185), (87641, 87651, 87661, 87671), (87965, 87975, 87985, 87995), (8X227, 8X237, 8X247, 8X257), (8E947, 8E957, 8E967, 8E977), (904E5, 90505, 90515, 90525), (9421E, 9422E, 9423E, 9424E), (94787, 94797, 947X7, 947E7), (96257, 96267, 96277, 96287), (98945, 98955, 98965, 98975), (99577, 99587, 99597, 995X7), (9E3E1, 9E401, 9E411, 9E421), (X481E, X482E, X483E, X484E), (X7E07, X7E17, X7E27, X7E37), (X856E, X857E, X858E, X859E), (X9215, X9225, X9235, X9245), (X98E1, X9901, X9911, X9921), (XX935, XX945, XX955, XX965), (E0E3E, E0E4E, E0E5E, E0E6E), (EX26E, EX27E, EX28E, EX29E), ...

(p, p+2, p+6, p+8, p+10) prime quintuplets: (5, 7, E, 11, 15), (E, 11, 15, 17, 1E), (85, 87, 8E, 91, 95), (X35, X37, X3E, X41, X45), (9365, 9367, 936E, 9371, 9375), (E2X5, E2X7, E2XE, E2E1, E2E5), (101XE, 101E1, 101E5, 101E7, 101EE), (10X7E, 10X81, 10X85, 10X87, 10X8E), (21405, 21407, 2140E, 21411, 21415), (2802E, 28031, 28035, 28037, 2803E), (6E515, 6E517, 6E51E, 6E521, 6E525), (7EX85, 7EX87, 7EX8E, 7EX91, 7EX95), (80675, 80677, 8067E, 80681, 80685), (9532E, 95331, 95335, 95337, 9533E), (98965, 98967, 9896E, 98971, 98975), (XX4X5, XX4X7, XX4XE, XX4E1, XX4E5), (EE355, EE357, EE35E, EE361, EE365), (10E68E, 10E691, 10E695, 10E697, 10E69E), (1388X5, 1388X7, 1388XE, 1388E1, 1388E5), (149465, 149467, 14946E, 149471, 149475), (15504E, 155051, 155055, 155057, 15505E), (17221E, 172221, 172225, 172227, 17222E), (1X5235, 1X5237, 1X523E, 1X5241, 1X5245), (210295, 210297, 21029E, 2102X1, 2102X5), (21X535, 21X537, 21X53E, 21X541, 21X545), (266705, 266707, 26670E, 266711, 266715), (26693E, 266941, 266945, 266947, 26694E), (27X6XE, 27X6E1, 27X6E5, 27X6E7, 27X6EE), (31067E, 310681, 310685, 310687, 31068E), (32463E, 324641, 324645, 324647, 32464E), (3401E5, 3401E7, 3401EE, 340201, 340205), (3545EE, 354601, 354605, 354607, 35460E), (362E4E, 362E51, 362E55, 362E57, 362E5E), (3X2865, 3X2867, 3X286E, 3X2871, 3X2875), (4079XE, 4079E1, 4079E5, 4079E7, 4079EE), (413885, 413887, 41388E, 413891, 413895), (433875, 433877, 43387E, 433881, 433885), (436565, 436567, 43656E, 436571, 436575), (447625, 447627, 44762E, 447631, 447635), (48666E, 486671, 486675, 486677, 48667E), (4871X5, 4871X7, 4871XE, 4871E1, 4871E5), (4X489E, 4X48X1, 4X48X5, 4X48X7, 4X48XE), (501335, 501337, 50133E, 501341, 501345), (547795, 547797, 54779E, 5477X1, 5477X5), (551E75, 551E77, 551E7E, 551E81, 551E85), (556415, 556417, 55641E, 556421, 556425), (55EE25, 55EE27, 55EE2E, 55EE31, 55EE35), (5X5875, 5X5877, 5X587E, 5X5881, 5X5885), (63X745, 63X747, 63X74E, 63X751, 63X755), (65E115, 65E117, 65E11E, 65E121, 65E125), (78596E, 785971, 785975, 785977, 78597E), (78X285, 78X287, 78X28E, 78X291, 78X295), (79896E, 798971, 798975, 798977, 79897E), (7X2EE5, 7X2EE7, 7X2EEE, 7X3001, 7X3005), (7X5X3E, 7X5X41, 7X5X45, 7X5X47, 7X5X4E), (80998E, 809991, 809995, 809997, 80999E), (87022E, 870231, 870235, 870237, 87023E), (8X3535, 8X3537, 8X353E, 8X3541, 8X3545), (8E378E, 8E3791, 8E3795, 8E3797, 8E379E), (94E92E, 94E931, 94E935, 94E937, 94E93E), (98783E, 987841, 987845, 987847, 98784E), (X06885, X06887, X0688E, X06891, X06895), (X0E4E5, X0E4E7, X0E4EE, X0E501, X0E505), (X37E95, X37E97, X37E9E, X37EX1, X37EX5), (X5744E, X57451, X57455, X57457, X5745E), (XE7025, XE7027, XE702E, XE7031, XE7035), (E1098E, E10991, E10995, E10997, E1099E), (E13735, E13737, E1373E, E13741, E13745), (E4161E, E41621, E41625, E41627, E4162E), (E4E58E, E4E591, E4E595, E4E597, E4E59E), (E4E805, E4E807, E4E80E, E4E811, E4E815), (E535X5, E535X7, E535XE, E535E1, E535E5), ...

(p, p+4, p+6, p+X, p+10) prime quintuplets: (7, E, 11, 15, 17), (81, 85, 87, 8E, 91), (10E7, 10EE, 1101, 1105, 1107), (2001, 2005, 2007, 200E, 2011), (3327, 332E, 3331, 3335, 3337), (9127, 912E, 9131, 9135, 9137), (9361, 9365, 9367, 936E, 9371), (E2X1, E2X5, E2X7, E2XE, E2E1), (21401, 21405, 21407, 2140E, 21411), (3X147, 3X14E, 3X151, 3X155, 3X157), (43487, 4348E, 43491, 43495, 43497), (4X617, 4X61E, 4X621, 4X625, 4X627), (105281, 105285, 105287, 10528E, 105291), (10X3E1, 10X3E5, 10X3E7, 10X3EE, 10X401), (1138E1, 1138E5, 1138E7, 1138EE, 113901), (118941, 118945, 118947, 11894E, 118951), (145367, 14536E, 145371, 145375, 145377), (151007, 15100E, 151011, 151015, 151017), (1611X7, 1611XE, 1611E1, 1611E5, 1611E7), (1750E1, 1750E5, 1750E7, 1750EE, 175101), (182607, 18260E, 182611, 182615, 182617), (1872E1, 1872E5, 1872E7, 1872EE, 187301), (1X4247, 1X424E, 1X4251, 1X4255, 1X4257), (1X8051, 1X8055, 1X8057, 1X805E, 1X8061), (262761, 262765, 262767, 26276E, 262771), (2817E7, 2817EE, 281801, 281805, 281807), (2E6171, 2E6175, 2E6177, 2E617E, 2E6181), (338831, 338835, 338837, 33883E, 338841), (353267, 35326E, 353271, 353275, 353277), (3X32E7, 3X32EE, 3X3301, 3X3305, 3X3307), (3E2017, 3E201E, 3E2021, 3E2025, 3E2027), (4137X1, 4137X5, 4137X7, 4137XE, 4137E1), (423E17, 423E1E, 423E21, 423E25, 423E27), (436247, 43624E, 436251, 436255, 436257), (447621, 447625, 447627, 44762E, 447631), (45E5X1, 45E5X5, 45E5X7, 45E5XE, 45E5E1), (473797, 47379E, 4737X1, 4737X5, 4737X7), (478907, 47890E, 478911, 478915, 478917), (483901, 483905, 483907, 48390E, 483911), (490231, 490235, 490237, 49023E, 490241), (4E4027, 4E402E, 4E4031, 4E4035, 4E4037), (51EE17, 51EE1E, 51EE21, 51EE25, 51EE27), (53X647, 53X64E, 53X651, 53X655, 53X657), (595801, 595805, 595807, 59580E, 595811), (599471, 599475, 599477, 59947E, 599481), (6170E1, 6170E5, 6170E7, 6170EE, 617101), (63XX07, 63XX0E, 63XX11, 63XX15, 63XX17), (6474E7, 6474EE, 647501, 647505, 647507), (65E111, 65E115, 65E117, 65E11E, 65E121), (6625E1, 6625E5, 6625E7, 6625EE, 662601), (743281, 743285, 743287, 74328E, 743291), (747377, 74737E, 747381, 747385, 747387), (77X157, 77X15E, 77X161, 77X165, 77X167), (781581, 781585, 781587, 78158E, 781591), (7X2EE1, 7X2EE5, 7X2EE7, 7X2EEE, 7X3001), (806907, 80690E, 806911, 806915, 806917), (812X91, 812X95, 812X97, 812X9E, 812XX1), (82X647, 82X64E, 82X651, 82X655, 82X657), (847E81, 847E85, 847E87, 847E8E, 847E91), (88E757, 88E75E, 88E761, 88E765, 88E767), (8X2917, 8X291E, 8X2921, 8X2925, 8X2927), (905091, 905095, 905097, 90509E, 9050X1), (969E31, 969E35, 969E37, 969E3E, 969E41), (9E1707, 9E170E, 9E1711, 9E1715, 9E1717), (9E63E1, 9E63E5, 9E63E7, 9E63EE, 9E6401), (9E6EX1, 9E6EX5, 9E6EX7, 9E6EXE, 9E6EE1), (X230X1, X230X5, X230X7, X230XE, X230E1), (X29617, X2961E, X29621, X29625, X29627), (X30XE7, X30XEE, X30E01, X30E05, X30E07), (X31287, X3128E, X31291, X31295, X31297), (X51857, X5185E, X51861, X51865, X51867), (X8E921, X8E925, X8E927, X8E92E, X8E931), (X95141, X95145, X95147, X9514E, X95151), (E33431, E33435, E33437, E3343E, E33441), (E41617, E4161E, E41621, E41625, E41627), (E4E587, E4E58E, E4E591, E4E595, E4E597), (E76571, E76575, E76577, E7657E, E76581), (E923E1, E923E5, E923E7, E923EE, E92401), (EX4957, EX495E, EX4961, EX4965, EX4967), ...

(p, p+4, p+6, p+X, p+10, p+14) prime sextuplets: (7, E, 11, 15, 17, 1E), (81, 85, 87, 8E, 91, 95), (9361, 9365, 9367, 936E, 9371, 9375), (E2X1, E2X5, E2X7, E2XE, E2E1, E2E5), (21401, 21405, 21407, 2140E, 21411, 21415), (447621, 447625, 447627, 44762E, 447631, 447635), (65E111, 65E115, 65E117, 65E11E, 65E121, 65E125), (7X2EE1, 7X2EE5, 7X2EE7, 7X2EEE, 7X3001, 7X3005), (E41617, E4161E, E41621, E41625, E41627, E4162E), (E4E587, E4E58E, E4E591, E4E595, E4E597, E4E59E), ...

Largest known prime number Edit

The largest known prime is a Mersenne prime 223,7XE,125−1, it has 7,870,133 digits, and its value is 174,164,383,313,720,093,6E1,098, ... (7,870,0E3 other digits) ... ,997,379,395,52E,129,858,481,227 (the first 20 digits and the last 20 digits are shown).

Classes of prime numbers Edit

  • By formula:
    • Fermat primes: of the form 22n + 1
      • Generalized Fermat primes base b: of the form b2n + 1
    • Mersenne primes: of the form 2p − 1 with prime p
      • Generalized Mersenne primes (Generalized repunit primes) base b: of the form (bp − 1)/(b − 1)
    • Double Mersenne primes: of the form 22p − 1 − 1 with prime p
    • Wagstaff primes: of the form (2p + 1)/3 with odd prime p
      • Generalized Wagstaff primes base b: of the form (bp + 1)/(b + 1) with odd prime p
    • Factorial primes: of the form n! ± 1
    • Primorial primes: of the form p# ± 1 with prime p
    • Proth primes: of the form k×2n + 1 with odd k and 2n > k
      • Generalized Proth primes base b: of the form k×bn + 1 with k not divisible by b and bn > k
    • Riesel primes: of the form k×2n − 1 with odd k and 2n > k
      • Generalized Riesel primes base b: of the form k×bn − 1 with k not divisible by b and bn > k
    • Pythagorean primes: of the form 4n + 1 (i.e. end with 1 or 5)
    • Gaussian primes with no imaginary part: of the form 4n−1 (i.e. end with 3, 7 or E)
    • Eisenstein primes with no imaginary part: of the form 3n−1 (i.e. end with 2, 5 or E)
    • Pierpont primes: of the form 2m×3n + 1
    • Cullen primes: of the form n×2n + 1
      • Generalized Cullen primes base b: of the form n×bn + 1 with nb−1
    • Woodall primes: of the form n×2n − 1
      • Generalized Woodall primes base b: of the form n×bn − 1 with nb−1
  • By size:

The smallest titanic prime is 10EEE+X97, and there are only 26 known megaprimes and 2 known mega-PRPs (no beva-(probable) primes or above are known, in fact, even no primes or PRPs with at least 107 digits are known, the largest known prime has “only” 7,870,133 digits), the smallest known megaprime is 3×23,762,E96+1, it has 1,018,16E digits, this prime is found by the 321 project, it is a Proth prime and a Pierpont prime, besides, both of the two known mega-PRPs are Wagstaff PRPs (of the form (2n+1)/3), and the exponents n of them are 4,578,17E and 4,58X,897.


Cite error: <ref> tags exist, but no <references/> tag was found
Community content is available under CC-BY-SA unless otherwise noted.