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A005234 Primorial primes: primes p such that 1 + product of primes up to p is prime.
(Formerly M0669)
+0
19
2, 3, 5, 7, 11, 31, 379, 1019, 1021, 2657, 3229, 4547, 4787, 11549, 13649, 18523, 23801, 24029, 42209, 145823, 366439, 392113 (list; graph; listen)
OFFSET

1,1

REFERENCES

C. K. Caldwell and Y. Gallot, On the primality of n!+-1 and 2*3*5*...*p+-1, Math. Comp., 71 (2001), 441-448.

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 211, p. 61, Ellipses, Paris 2008.

H. Dubner, A new primorial prime, J. Rec. Math., 21 (No. 4, 1989), 276.

R. K. Guy, Unsolved Problems in Number Theory, Section A2.

Paulo Ribenboim, The New Book of Prime Number Records, p. 13.

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

LINKS

C. K. Caldwell, Primorial Primes

R. Ondrejka, The Top Ten: a Catalogue of Primal Configurations

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

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

CROSSREFS

A014545 gives same sequence in another form, namely values of n such that 1 + product of first n primes is prime. Cf. A002110, A006862, A006794, A057704. A018239 gives the actual primes.

Sequence in context: A119388 A093487 A067933 this_sequence A141500 A059999 A040130

Adjacent sequences: A005231 A005232 A005233 this_sequence A005235 A005236 A005237

KEYWORD

nonn,hard,nice

AUTHOR

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

EXTENSIONS

42209 sent in by Chris Nash (chrisnash(AT)cwix.com).

145823 discovered and sent in by Arlin Anderson (starship1(AT)gmail.com) and Don Robinson (donald.robinson(AT)itt.com), Jun 01 2000

366439, 392113 from Eric Weisstein (eric(AT)weisstein.com), Mar 13 2004 (based on information in A057704)

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Last modified December 4 23:11 EST 2009. Contains 170347 sequences.


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