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The Eddington number 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.[1] 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 $$g_{\omega^{\omega^32+3}2+\omega^{\omega^32+1}2}(4)$$

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