Wolstenholme Prime
المؤلف:
Sloane, N. J. A
المصدر:
Sequence A088164 in "The On-Line Encyclopedia of Integer Sequences."
الجزء والصفحة:
...
31-8-2020
895
Wolstenholme Prime
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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