name

symbol

value

remarks

Euler-Napier constant and associated optimal numbers, e2 = e e ; e3 = e e e ; e4 = e e e e

e

2.718281828459042

e 4 1 / a a ( 9 / 2 ) 1 / a P sin 2 θ

Archimedes constant π and π a 6 / ( 1 / g 1 1 ) 3 / ( 1 g 1 g 2 g 3 / 6 ) 3 + ( q / ( 1 + 1 / Δ E d ) ) 2 / g 2

π

3.14159265358979

π a ( a 2 137 2 ) 1 / 2

Euler-Mascheroni constant γ / π = Γ / a ln Φ / Φ 2 ln ζ ( 3 )

γ

0.57721566490153

Φ π / γ e Φ 2 a / 10

Golden ratio and Black Body Photon Constant ϕ = λ / l p h = ( 16 π ζ ( 3 ) ) 1 / 3

Φ

1.61803398874990

ζ ( 3 ) 1.20205691

Wien parameter W 5 = h c / k B T l W i e n = 5 ( 1 e W 5 ) a / 137 g 1 3 ln 2 4 ln g 1

w 5

4.96514245

W 3 2.821439372

Relative Radiation Ratio u C M B + C N B / u C M B = 1 + 3 ( 7 / 8 ) ( 4 / 11 ) 4 / 3 p t n t / H p W 1

y

1.681321953

p W 1 = 1903 (A001220)

Scale-factor 8 π 2 / ln 2 ( 16 q ) 3 i π / i / g 3 ( i π / i 1 ) / 4 q π Δ E d / 8 ( Φ 4 / g 2 ) 2

j

113.9106346

[5] j T m a m / T C M B

Lucas Large Prime Number P 3 + 7 a 7 ( a ) 7 + 127 P / a w a ( ( a ) 127 / P 3 ) 1 / 7 n 3

n L

2127 - 1

[7] Cb. Hier. 3,7,127,2127 - 1

Eddington Large Number ( 1 / g 1 1 ) τ 2 / μ 2 1839 / 2 d e n t ( 6 / π ) τ 2 / μ 2 1 ( 4 π ) 2 a / 1839

n E d

136 × 2256

[10]

Eddington Proton-Electron mass ratio p E d = ( 136 + Δ E d ) / ( 136 Δ e d ) Δ e d = ( 136 2 40 ) 1 / 2

p E d

1847.599459

[10] Δ e d = ( 137 2 40 ) 1 / 2

Maximal known Euler idoneal (“Suitable”) Number p E d H 5 / n t 2 p 00 3 ( H Φ ) 3 / a 7 / 2 sin θ

s 65

1848

OEIS (A000926)

Extended Maximal Number of Intersection of Diagonals from a 16-gone 1836 ( 3 a 3 / 20 q ) 1 / 2 / ( g 2 g 3 ) 2

p 00

1836

OEIS (A000332+n)

Proton/Electron mass ratio m p / m e n t / p t ( n t p t ) 1 / ( 26 p t / n t ) 2 ( ( 4 π p W / p t ) 2 ) 1 / p t n t

p t

1836.15267343

0.06 ppb

Wyler Proton/Electron mass ratio p W = 6 π 5 ( a p t / 137 ) 2 / H p t ( s 65 p 00 / p E d ) 3 / H ( H p 00 7 ) 1 / 2 / p t 3

p W

1836.118109

P / a w a n t 3 ( p W / p t ) 5

Hydrogen/Electron mass ratio H 8 e 2 e 495 / g 1 g 2 g 3

H

1837.15266014

0.06 ppb

Relativistic correction factor 1 / ( H p t )

β

1.000026597

0.1 ppb

Neutron/Electron mass ratio n t ( π 2 W 5 / 4 ) 3 p t + 1 + 1 / g t 0 p t ( 61 / 60 ) 1 / 12 ( p t H ) d e / β 2

n t

1838.6836617

0.5 ppb

Planck ratio m P / m e = P 2 64 ( a / 4 π ) 3 β 2 p t / n t ( sin θ ) a d e / 2

P

2.2389015907 × 1022

ppb [5]

Lucas Gravitational Proton/Electron mass ratio P / n L 2 ( a / 137 ) 2 p t / p W q 6

p G

1831.531181

β u 30 a / 137

Bisection of Rule 23 Wolfram series (R23W) u d = 1 + d ( 2 d + 1 ) for d = 30

u 30

1831

EOIS(A266438)

Combined R23W: u ' d = u 2 D = 2 ( d + 3 ) = 1 + 2 ( d + 3 ) + 8 ( d + 3 ) 2 for d = 12

u ' 12

1831

30D to 12D

R23W for d = 8: Eddington’s formula [10] : u 8 = 136 + 1

u 8

137

v 8 = 495 + 496

Combined R23W u ' 1 = u 2 × ( 1 + 3 ) for d = 1: Hol Sweeping 1D Absolute Space

u ' 1

137

12D to 1D

u 2 d = 1 + 2 d ( 4 d + 1 ) Bisection of odd central polygonal numbers for d = 4

a 00

137

OEIS (A188135)

Eddington-Atiyah constant 2 7 + 2 3 + 2 0

a 00

137

from three algebra [30]

Maximal number of zones defined by 16 straight lines in a plane

a 00

137

OEIS (AA000124)

Number of partitions of 20 that do not contain 1 as a part

a 00

137

OEIS (A002865)