## FANDOM

114 Pages

• $\pi$ = 3.184809 493E91 866457 3X6211 ... (this number is known to be transcendental)
• e = 2.875236 069821 9EX719 71009E ... (this number is known to be transcendental)
• $\tau$ = $2\pi$ = 6.349416 967E63 5108E2 790423 ... (this number is known to be transcendental)
• $\sqrt{7}$ = 2.78EX37 0EE138 X90059 368336 ...
• $\sqrt{8}$ = $2\sqrt{2}$ = 2.9E3632 1813E4 E27320 9X14X9 ...
• $\sqrt{\mathcal{X}}$ = 3.1E44EX 5E6609 27E326 833X86 ...
• $\sqrt{\mathcal{E}}$ = 3.397164 684294 8XE2E8 1EX94X ...
• $\sqrt{10}$ = $2\sqrt{3}$ = 3.569E73 EE7152 0982X7 7945XX ...
• $\sqrt{10}$ = 100.4 = 2.358170 9XX919 6E5574 34641E ...
• $\sqrt{10}$ = 100.3 = 1.X40206 532E36 X73495 X09198 ...
• $\sqrt{10}$ = 100.2 = 1.61X741 X0891E 36EX86 8E4136 ...
• $\sqrt{10}$ = 100.1 = 1.2916X1 9411X8 585437 376313 ...
• Golden ratio $\phi$ = $\frac{\sqrt{5}+1}{2}$ = 1.74EE67 72802X 46X6X1 865307 ...
• Silver ratio $\delta_S$ = $\sqrt{2}+1$ = 2.4E7917 0X07E8 573770 4E0854 ...
• Bronze ratio $S_3$ = $\frac{\sqrt{11}+3}{2}$ = 3.377243 262773 297X8X 145586 ...
• Supergolden ratio $\psi$ = $\frac{1 + \sqrt{\frac{25 + 3\sqrt{79}}{2}} + \sqrt{\frac{25 - 3\sqrt{79}}{2}}}{3}$ = 1.570610 2EX83E 671699 9E0780 ...
• Plastic number $\rho$ = $\sqrt{\frac{9 + \sqrt{59}}{16}} + \sqrt{\frac{9 - \sqrt{59}}{16}}$ = 1.3X9142 75E896 79EX0X 349146 ...
• Tribonacci constant $\xi_3$ = $\frac{1+\sqrt{17+3\sqrt{29}}+\sqrt{17-3\sqrt{29}}}{3}$ = 1.X0X354 9X52E8 380557 38X342 ...
• $\frac{1}{\pi}$ = 0.39X058 2886E3 742178 522877 ... (this number is known to be transcendental)
• $\frac{1}{e}$ = 0.44E842 160564 X444E6 X08E59 ... (this number is known to be transcendental)
• Gelfond's constant $e^\pi$ = 1E.183149 E4X351 682985 97E590 ... (this number is known to be transcendental)
• ii = $\frac{1}{\sqrt{e^\pi}}$ = 0.25E271 109778 366X20 XX4005 ... (this number is known to be transcendental)
• Ramanujan's constant = $e^{\pi \sqrt{117}}$ = 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 $q=e^{2\pi i t}$: 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 = $\sum_{k=1}^{\infty}(10^{-k!})$ = 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)
• Apéry's constant $\zeta(3)$ = 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 $\zeta(5)$, $\zeta(7)$, $\zeta(9)$ and $\zeta(\mathcal{E})$ is irrational, but none of them is known to be irrational)
• Lévy's constant $\gamma$ = $e^{\pi^2/(10\ln2)}$ = 3.338756 9X479X 99X939 7714XX ...
• Mills' constant A = 1.381507 56153E 408X1E X7E71X ... (assuming the Riemann Hypothesis is true)
• Brun's constant B2 = 1.X9XE25 097070 ... (only 10 digits after the dozenal point are known)

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. $\pi$ and e are transcendental, but it is unknown whether Euler–Mascheroni constant $\gamma$ is transcendental or not), no numbers above (except Champernowne constant and Copeland–Erdős constant) are known to be normal, and it is conjectured that $\pi$, e, Euler–Mascheroni constant $\gamma$, $\sqrt{2}$, ln 2 and some other numbers are all normal, but none has proof, however, not all irrational number are normal, the number 0.1101001000100001000001... is irrational, but not normal.

Community content is available under CC-BY-SA unless otherwise noted.