Eddington number

The Eddington number or Eddington's numberKasner and Newman. Mathematics and the Imagination Originally published by Simon and Shuster, 1940. Dover Edition published in 2001. ISBN 978-1556151040 p.32 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 	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 	\(g_{\omega^{\omega^32+3}2+\omega^{\omega^32+1}2}(4)\)	\(g_{\omega^{\omega^32+3}2+\omega^{\omega^32+1}2}(4)\)
== Sources ==
== See also ==
ja:エディントン数
Category:Numbers
Category:Class 2
Category:Eponymous numbers
Category:Non-powers
Category:Numbers with 30 to 100 digits
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