1,1

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.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 52.

C. Clawson, Mathematical Mysteries, Plenum Press, 1996, p. 180.

R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see p. 29.

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, th. 80.

P. Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 2nd ed., 1989, p. 277.

I. Vardi, Computational Recreations in Mathematica. Addison-Wesley, Redwood City, CA, 1991, p. 73.

D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, 163.

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

P. Zimmermann, RECORDS FOR PRIME NUMBERS

Eric Weisstein's World of Mathematics, Integer Sequence Primes

Wikipedia, Wilson prime

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]

Cf. A007619.

Sequence in context: A122900 A145557 A012033 this_sequence A157250 A155185 A009157

Adjacent sequences: A007537 A007538 A007539 this_sequence A007541 A007542 A007543

nonn,hard,bref,nice

N. J. A. Sloane (njas(AT)research.att.com).

Believed to be infinite. Next term known to be > 4*10^8.