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A277587
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Decimal expansion of the sum of the reciprocals of the Wieferich primes.
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0
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0, 0, 1, 1, 9, 9, 7, 3, 2, 2, 2, 3, 1, 0, 3, 2, 8, 8
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OFFSET
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0,5
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COMMENTS
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A heuristic argument predicts about log(log(x)) Wieferich primes below some number x (see for example Dorais, Klyve, 2011, result 14). PrimeGrid has searched to about 2.7 * 10^18 as of Apr 03 2021 without finding a third Wieferich prime, so the constant is known to 18 places after the decimal point.
It seems that if there are only finitely many Wieferich primes, then the constant is rational and if there are infinitely many Wieferich primes, then the constant is irrational.
The period lengths of 1/1093 and 1/3511 are 1092 and 3510, respectively (cf. Garza, Young, 2004).
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LINKS
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PrimeGrid, Subproject status (See "Wieferich and Wall-Sun-Sun Prime Search" at the bottom).
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EXAMPLE
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1/1093 + 1/3511 = 4604/3837523 ~ 0.001199732223103288...
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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