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).
See also
Central Binomial Coefficient,
Integer Sequence Primes,
Wolstenholme
Number,
Wolstenholme's Theorem
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References
McIntosh, R. email to Paul Zimmermann. 9 Mar 2004. http://www.loria.fr/~zimmerma/records/Wieferich.status.Sloane,
N. J. A. Sequence A088164 in "The
On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Wolstenholme Prime
Cite this as:
Weisstein, Eric W. "Wolstenholme Prime."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/WolstenholmePrime.html
Subject classifications
