The Eddington number[1] or Eddington's number[2] is \(N_\text{Edd} = 136 \cdot 2^{256} \approx 1.575 \times 10^{79}\), which Arthur Eddington asserted to be the exact number of protons in the observable universe. 136 is the reciprocal of the fine structure constant, or at least the best available estimation at the time. It is now known to be about \(1/137.035999074\); Eddington's original value, if not his whole argument, is incorrect.
Its full decimal expansion is
- 15,747,724,136,275,002,577,605,653,961,181,555,468,044,717,914,527,116,709,366,231,425,076,185,631,031,296
Approximations[]
Notation | Lower bound | Upper bound |
---|---|---|
Scientific notation | \(1.574\times10^{79}\) | \(1.575\times10^{79}\) |
Arrow notation | \(183\uparrow35\) | \(3\uparrow166\) |
Steinhaus-Moser Notation | 47[3] | 48[3] |
Copy notation | 1[80] | 2[80] |
Taro's multivariable Ackermann function | A(3,260) | A(3,261) |
Pound-Star Notation | #*(7,3,8,3,5,3,1)*7 | #*(5,10,5,3,2)*12 |
BEAF | {183,35} | {3,166} |
Hyper-E notation | 136E[2]3#3 | |
Bashicu matrix system | (0)(0)(0)(0)[89089] | (0)(0)(0)(0)[89090] |
Hyperfactorial array notation | 58! | 59! |
Fast-growing hierarchy | \(f_2(255)\) | \(f_2(256)\) |
Hardy hierarchy | \(H_{\omega^2}(255)\) | \(H_{\omega^2}(256)\) |
Slow-growing hierarchy | \(g_{\omega^{\omega^32+3}2+\omega^{\omega^32+1}2}(4)\) |
Sources[]
- ↑ [1]
- ↑ Kasner and Newman. Mathematics and the Imagination Originally published by Simon and Shuster, 1940. Dover Edition published in 2001. ISBN 978-1556151040 p.32
See also[]
Large numbers in science
Sagan's number · Avogadro's number · Eddington number · Planck units · Promaxima · Poincaré recurrence time · Universe size