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According to Eddington, the exact number of protons in the universe, where 136 was the reciprocal of the fine structure constant as best as it could be measured in his time.
Eddington Number
See also
Large Number, Wyler's ConstantExplore with Wolfram|Alpha
References
Hardy, G. H. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York: Chelsea, pp. 15 and 49, 1999.Referenced on Wolfram|Alpha
Eddington NumberCite this as:
Weisstein, Eric W. "Eddington Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EddingtonNumber.html