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Wolstenholme prime

In mathematics, a Wolstenholme prime is a certain kind of prime number. A prime p is called a Wolstenholme prime iff the following condition holds:

{{2p-1}\choose{p-1}} \equiv 1 \pmod{p^4}

Wolstenholme primes are named after mathematician Joseph Wolstenholme, who proved Wolstenholme's theorem, the equivalent statement for p3 in 1862, following Charles Babbage who showed the equivalent for p2 in 1819.

The only known Wolstenholme primes so far are 16843 and 2124679 ; any other Wolstenholme prime must be greater than 6.4 · 108.

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Science Fair Project Encyclopedia Contents Page
12-03-2008 10:22:39
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