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Date: 28-7-2020
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Date: 26-9-2020
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Date: 18-10-2020
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A prime is called a Wolstenholme prime if the central binomial coefficient
(1) |
or equivalently if
(2) |
where is the th Bernoulli number and the congruence is fractional.
A prime is a Wolstenholme prime if and only if
(3) |
where the congruence is again fractional.
The only known Wolstenholme primes are 16843 and 2124679 (OEIS A088164). There are no others up to (McIntosh 2004).
REFERENCES:
McIntosh, R. email to Paul Zimmermann. 9 Mar 2004. https://www.loria.fr/~zimmerma/records/Wieferich.status.
Sloane, N. J. A. Sequence A088164 in "The On-Line Encyclopedia of Integer Sequences."
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