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A007540 Wilson primes: primes p such that (p-1)! == -1 mod p^2.
(Formerly M3838)
+0
10
5, 13, 563 (list; graph; listen)
OFFSET

1,1

COMMENT

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.

REFERENCES

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.

LINKS

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

CROSSREFS

Cf. A007619.

Adjacent sequences: A007537 A007538 A007539 this_sequence A007541 A007542 A007543

Sequence in context: A067135 A122900 A012033 this_sequence A009157 A012032 A121228

KEYWORD

nonn,hard,bref,nice

AUTHOR

njas

EXTENSIONS

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

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Last modified May 16 23:01 EDT 2008. Contains 139884 sequences.


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