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• e = 2.875236 069821 9EX719 71009E ... (this number is known to be transcendental)
• ${\displaystyle \tau}$ = ${\displaystyle 2\pi}$ = 6.349416 967E63 5108E2 790423 ... (this number is known to be transcendental)
• Euler–Mascheroni constant ${\displaystyle \gamma}$ = 0.6E1518 8X6760 E381E7 543345 ...
• ${\displaystyle \sqrt{3}}$ = 1.894E97 EE9687 04X153 9X82E5 ...
• ${\displaystyle \sqrt5}$ = 2.29EE13 254058 919183 50X612 ...
• ${\displaystyle \sqrt{6}}$ = 2.548875 21E2X3 69X1E8 741X63 ...
• ${\displaystyle \sqrt{7}}$ = 2.78EX37 0EE138 X90059 368336 ...
• ${\displaystyle \sqrt {8}}$ = ${\displaystyle 2\sqrt{2}}$ = 2.9E3632 1813E4 E27320 9X14X9 ...
• ${\displaystyle \sqrt{\mathcal{X}}}$ = 3.1E44EX 5E6609 27E326 833X86 ...
• ${\displaystyle \sqrt{\mathcal{E}}}$ = 3.397164 684294 8XE2E8 1EX94X ...
• ${\displaystyle \sqrt{10}}$ = ${\displaystyle 2\sqrt{3}}$ = 3.569E73 EE7152 0982X7 7945XX ...
• ${\displaystyle \sqrt[3]{2}}$ = 20.4 = 1.315188 11X39X X22801 X49414 ...
• ${\displaystyle \sqrt[4]{2}}$ = 20.3 = 1.232E49 502548 E9E65E 2E6377 ...
• ${\displaystyle \sqrt[6]{2}}$ = 20.2 = 1.157745 872895 66E6E2 3296X5 ...
• ${\displaystyle \sqrt[3]{10}}$ = 100.4 = 2.358170 9XX919 6E5574 34641E ...
• ${\displaystyle \sqrt[4]{10}}$ = 100.3 = 1.X40206 532E36 X73495 X09198 ...
• ${\displaystyle \sqrt[6]{10}}$ = 100.2 = 1.61X741 X0891E 36EX86 8E4136 ...
• ${\displaystyle \sqrt[10]{10}}$ = 100.1 = 1.2916X1 9411X8 585437 376313 ...
• Golden ratio ${\displaystyle \phi}$ = ${\displaystyle \frac{\sqrt{5} +1}{2}}$ = 1.74EE67 72802X 46X6X1 865307 ...
• Silver ratio ${\displaystyle \delta_S}$ = ${\displaystyle \sqrt{2}+1}$ = 2.4E7917 0X07E8 573770 4E0854 ...
• Bronze ratio ${\displaystyle M_3}$ = ${\displaystyle \frac{\sqrt{11}+3}{2}}$ = 3.377243 262773 297X8X 145586 ...
• Supergolden ratio ${\displaystyle \psi}$ = ${\displaystyle \frac{1 + \sqrt[3]{\frac{25 + 3\sqrt{79}}{2}} + \sqrt[3]{\frac{25 - 3\sqrt{79}}{2}}}{3}}$ = 1.570610 2EX83E 671699 9E0780 ...
• Plastic number ${\displaystyle \rho}$ = ${\displaystyle \sqrt[3]{\frac{9 + \sqrt{59}}{16}} + \sqrt[3]{\frac{9 - \sqrt{59}}{16}}}$ = 1.3X9142 75E896 79EX0X 349146 ...
• Tribonacci constant ${\displaystyle \xi_3}$ = ${\displaystyle \frac{1+\sqrt[3]{17+3\sqrt{29}}+\sqrt[3]{17-3\sqrt{29}}}{3}}$ = 1.X0X354 9X52E8 380557 38X342 ...
• Triangular root of 2 = ${\displaystyle \frac{\sqrt{15}-1}{2}}$ = 1.68X443 86X184 290224 26E1X6 ...
• ${\displaystyle \frac{1}{\pi}}$ = 0.39X058 2886E3 742178 522877 ... (this number is known to be transcendental)
• ${\displaystyle \frac{1}{e}}$ = 0.44E842 160564 X444E6 X08E59 ... (this number is known to be transcendental)
• Gelfond's constant ${\displaystyle e^\pi}$ = 1E.183149 E4X351 682985 97E590 ... (this number is known to be transcendental)
• Gelfond–Schneider constant ${\displaystyle 2^{\sqrt{2}}}$ = 2.7E9451 92684E 205155 351558 ... (this number is known to be transcendental)
• ii = ${\displaystyle \frac{1}{\sqrt{e^\pi}}}$ = 0.25E271 109778 366X20 XX4005 ... (this number is known to be transcendental)
• Ramanujan's constant = ${\displaystyle e^{\pi\sqrt{117}}}$ = 15059 399520 36851E.EEEEEE EEEEE5 391X28 99X944 ... (very close to an integer, this integer is 26X6803+520, given by the coefficients of modular function j as power series in ${\displaystyle q=e^{2\pi i t}}$: 1, 520, 95E30, 7246628, 201551716, 3E10368000, 546E0X82248, 5880X2000000, 50129X8E61853, 3904375971E140, 258313492001830, 156E10001X400000, 95X677EEX7915E66, 488E812838X800000, ..., besides, 117 is the largest Heegner number, there are only 9 Heegner numbers, and they are 1, 2, 3, 7, E, 17, 37, 57, 117) (this number is known to be transcendental)
• ln 2 = 0.839912 483369 XE2137 42X346 ... (this number is known to be transcendental)
• ln 3 = 1.12249X 871651 3489E9 024604 ... (this number is known to be transcendental)
• ln 10 = 2.376X4X 2E577E 9643X6 2071X6 ... (this number is known to be transcendental)
• log e = 0.49E494 439904 549679 E59E5E ... (this number is known to be transcendental)
• log 2 = 0.34201E 20X371 X7X232 04520X ... (this number is known to be transcendental)
• log 3 = 0.537E81 7X3498 283757 E317X2 ... (this number is known to be transcendental)
• log 4 = 0.68403X 418723 938464 08X419 ... (this number is known to be transcendental)
• log 5 = 0.79324X 517079 42X898 265X68 ... (this number is known to be transcendental)
• log 6 = 0.879EX0 9E184X 141989 E769E1 ... (this number is known to be transcendental)
• log 7 = 0.949223 8X4XX7 8X1E96 X67297 ... (this number is known to be transcendental)
• log 8 = 0.X06059 626X95 7E6696 113627 ... (this number is known to be transcendental)
• log 9 = 0.X73E43 386974 5472E3 X63385 ... (this number is known to be transcendental)
• log X = 0.E15269 72542E 2X8E0X 2XE077 ... (this number is known to be transcendental)
• log E = 0.E6E5XX E08546 192E29 605377 ... (this number is known to be transcendental)
• log2e = 1.538E88 385XX6 96568X 18E862 ... (this number is known to be transcendental)
• log23 = 1.702994 801X64 X27179 734E85 ... (this number is known to be transcendental)
• log210 = 3.702994 801X64 X27179 734E85 ... (this number is known to be transcendental)
• sin 1 = 0.X1208X X92234 12E470 074934 ... (this number is known to be transcendental)
• cos 1 = 0.659786 059E60 8074X8 682736 ... (this number is known to be transcendental)
• tan 1 = 1.68324X 669888 E2050X X90009 ... (this number is known to be transcendental)
• sinh 1 = 1.2128E7 E6473X 599111 461681 ... (this number is known to be transcendental)
• cosh 1 = 1.66253X 1050X3 421608 26X61X ... (this number is known to be transcendental)
• tanh 1 = 0.91804E E6X122 4187E5 7369XX ... (this number is known to be transcendental)
• Liouville constant c = ${\displaystyle \sum_{k=1}^{\infty}(10^{-k!})}$ = 0.110001 000000 000000 000001 ... (this number is known to be transcendental)
• Champernowne constant C10 = 0.123456 789XE1 011121 314151 617181 91X1E2 0... (this number is known to be transcendental and normal)
• Copeland–Erdős constant 0.2357E1 115171 E25273 135373 E454E5 1575E6 1676E7 5... (this number is known to be normal)
• Conway's constant ${\displaystyle \lambda}$ = 1.3786E8 X500E1 032785 6650E6 ... (this number is an algebraic number with degree 5E)
• Prouhet–Thue–Morse constant ${\displaystyle \tau}$ = 0.4E4879 18XX67 685435 982056 ... (this number is known to be transcendental)
• Komornik–Loreti constant q = 1.954405 141105 7X0760 X38227 ... (this number is known to be transcendental)
• ${\displaystyle \zeta(2)}$ = ${\displaystyle \frac{\pi^2}{6}}$ = 1.78X542 97X561 05370X 330717 ... (this number is known to be transcendental)
• Apéry's constant ${\displaystyle \zeta(3)}$ = 1.2511X2 81XXXX 589757 692336 ... (this number is known to be irrational, but not known whether or not it is transcendental, also it is known that at least one of ${\displaystyle \zeta(5)}$, ${\displaystyle \zeta(7)}$, ${\displaystyle \zeta(9)}$ and ${\displaystyle \zeta(\mathcal{E})}$ is irrational, but none of them is known to be irrational)
• ${\displaystyle \zeta(4)}$ = ${\displaystyle \frac{\pi^4}{76}}$ = 1.0EX307 X37995 919XE1 8012E3 ... (this number is known to be transcendental)
• Catalan's constant G = 0.XEX956 737E3X 6XE083 X55465 ...
• Artin's constant CArtin = 0.45X242 0XE766 13448X EX9069 ...
• Khinchin's constant K0 = 2.828564 85E404 426608 2X7290 ...
• Lévy's constant ${\displaystyle \gamma}$ = ${\displaystyle e^{\pi^2/(10\ln2)}}$ = 3.338756 9X479X 99X939 7714XX ... (this number is known to be transcendental)
• Khinchin–Lévy constant = ${\displaystyle \frac{\pi^2}{10\ln2}}$ = 1.22X484 466267 593745 9637X5 ... (this number is known to be transcendental)
• Mills' constant A = 1.381507 56153E 408X1E X7E71X ... (assuming the Riemann Hypothesis is true)
• Vardi's constant E = 1.320408 9645X9 1E4692 412396 ...
• Brun's constant B2 = 1.X9XE25 097070 ... (only 10 digits after the dozenal point are known)
• Twin prime constant C2 = 0.7E0914 752669 928452 606598 ...
• Erdős–Borwein constant E = 1.734452 027104 885050 XX1X49 ...
• Reciprocal Fibonacci constant ${\displaystyle \psi}$ = 3.439X70 X11793 855644 5XX497 ... (this number is known to be irrational, but not known whether or not it is transcendental)
• Soldner's constant = 1.54EE71 391794 821836 6E6696 ...
• Glaisher-Kinkelin constant A = 1.34804X X7E731 8724E7 4X4253 ...
• Golomb-Dickman constant = 0.75XX13 434074 998279 990537 ...
• Landau–Ramanujan constant = 0.9206E3 7283X6 831700 X90E89 ...
• Laplace limit ${\displaystyle \epsilon}$ = 0.7E5279 2E56X9 E51235 50X813 ...
• Landau's totient constant = 1.40E192 06764X 633967 35409X ...
• Gauss's constant G = 0.X0229X 48XE08 83X3E5 232250 ... (this number is known to be transcendental)
• Omega constant ${\displaystyle \Omega}$ = 0.698034 95X760 082138 216097 ... (this number is known to be transcendental)
• Sierpinski constant K = 2.702X22 211432 1E6090 0XE801 ...
• Viswanath's constant ${\displaystyle \sigma(1)}$ = 1.1700XX 9709X7 ... (only 10 digits after the dozenal point are known)
• Bernstein's constant ${\displaystyle \beta}$ = 0.344171 784362 466129 046158 ...
• Backhouse's constant = 1.558120 5EX8X0 5502E4 59X201 ...
• 1st Feigenbaum constant ${\displaystyle \delta}$ = 4.804469 36X214 98X58X 598EE8 ...
• 2nd Feigenbaum constant ${\displaystyle \alpha}$ = 2.605036 X50951 E67149 639726 ...

Most of these numbers above are conjectured to be irrational, transcendental and normal, but all have no proof except the numbers with these notes (e.g. ${\displaystyle \pi }$, e, ${\displaystyle e^\pi}$, and ${\displaystyle 2^{\sqrt{2}}}$ are transcendental, and of course ${\displaystyle \sqrt{2}}$ and golden ratio ${\displaystyle \phi}$ are not transcendental, but it is unknown whether Euler–Mascheroni constant ${\displaystyle \gamma}$ is transcendental or not), no numbers above (except Champernowne constant and Copeland–Erdős constant) are known to be normal, and it is conjectured that ${\displaystyle \pi }$, e, Euler–Mascheroni constant ${\displaystyle \gamma}$, ${\displaystyle \sqrt{2}}$, ln 2, golden ratio ${\displaystyle \phi}$ and some other numbers are all normal, but none has proof, however, not all irrational number are normal, the number 0.11010010001000010000010000001... is irrational, but not normal.

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