Search: id:A007540
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%I A007540 M3838
%S A007540 5,13,563
%N A007540 Wilson primes: primes p such that (p-1)! == -1 mod p^2.
%C A007540 Suggested by the Wilson-Lagrange Theorem: An integer p > 1 is a prime 
               if and only if (p-1)! == -1 (mod p). Cf. Wilson quotients, A007619.
%D A007540 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A007540 A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, 
               p. 52.
%D A007540 C. Clawson, Mathematical Mysteries, Plenum Press, 1996, p. 180.
%D A007540 R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, 
               Springer, NY, 2001; see p. 29.
%D A007540 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 
               5th ed., Oxford Univ. Press, 1979, th. 80.
%D A007540 P. Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 
               2nd ed., 1989, p. 277.
%D A007540 I. Vardi, Computational Recreations in Mathematica. Addison-Wesley, Redwood 
               City, CA, 1991, p. 73.
%D A007540 D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. 
               Penguin Books, NY, 1986, 163.
%H A007540 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               WilsonPrime.html">Link to a section of The World of Mathematics.</
               a>
%H A007540 P. Zimmermann, <a href="http://www.loria.fr/~zimmerma/records/primes.html">
               RECORDS FOR PRIME NUMBERS</a>
%H A007540 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               IntegerSequencePrimes.html">Integer Sequence Primes</a>
%H A007540 Wikipedia, <a href="http://en.wikipedia.org/wiki/Wilson_prime">Wilson 
               prime</a>
%t A007540 lst={};Do[p=Prime[n];If[Mod[(p-1)!+1, p^2]==0, AppendTo[lst, p]], {n, 
               5!}];lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 25 
               2008]
%Y A007540 Cf. A007619.
%Y A007540 Sequence in context: A122900 A145557 A012033 this_sequence A157250 A155185 
               A009157
%Y A007540 Adjacent sequences: A007537 A007538 A007539 this_sequence A007541 A007542 
               A007543
%K A007540 nonn,hard,bref,nice
%O A007540 1,1
%A A007540 N. J. A. Sloane (njas(AT)research.att.com).
%E A007540 Believed to be infinite. Next term known to be > 4*10^8.

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