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About: Wilson quotient     Goto   Sponge   NotDistinct   Permalink

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Type: yago:Abstraction100002137yago:Arrangement107938773yago:Group100031264yago:Ordering108456993yago:WikicatIntegerSequencesyago:Sequence108459252yago:Series108457976 New Facet based on Instances of this Class

The Wilson quotient W(p) is defined as: If p is a prime number, the quotient is an integer by Wilson's theorem; moreover, if p is composite, the quotient is not an integer. If p divides W(p), it is called a Wilson prime. The integer values of W(p) are (sequence in the OEIS): W(2) = 1W(3) = 1W(5) = 5W(7) = 103W(11) = 329891W(13) = 36846277W(17) = 1230752346353W(19) = 336967037143579... It is known that where is the k-th Bernoulli number. Note that the first relation comes from the second one by subtraction, after substituting and .