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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. 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 48
Copy notation 1 2
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 136E3#3
Bashicu matrix system (0)(0)(0)(0) (0)(0)(0)(0)
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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