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A006794
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Primes p such that -1 + product of primes up to p is prime.
(Formerly M2474)
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17
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3, 5, 11, 13, 41, 89, 317, 337, 991, 1873, 2053, 2377, 4093, 4297, 4583, 6569, 13033, 15877
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OFFSET
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1,1
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COMMENTS
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Or, p such that primorial(p) - 1 is prime.
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REFERENCES
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C. K. Caldwell, On the primality of n! +- 1 and 2*3*5*...*p +- 1, Math. Comput. 64, 889-890, 1995.
C. K. Caldwell and Y. Gallot, On the primality of n!+-1 and 2*3*5*...*p +- 1, Math. Comp., 71 (2001), 441-448.
H. Dubner, Factorial and primorial primes, J. Rec. Math., 19 (No. 3, 1987), 197-203.
R. K. Guy, Unsolved Problems in Number Theory, Section A2.
R. Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, Arxiv preprint arXiv:1202.3670, 2012 - From N. J. A. Sloane, Jun 13 2012
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Table of n, a(n) for n=1..18.
C. K. Caldwell, Primorial Primes
Eric Weisstein's World of Mathematics, Primorial
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FORMULA
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a(n) = A000040(A057704(n))
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MATHEMATICA
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primorial[p_] := Product[Prime[k], {k, 1, PrimePi[p]}]; Select[Prime[Range[1900]], PrimeQ[primorial[#] - 1] &] (* From Jean-François Alcover, Mar 16 2011 *)
Transpose[With[{pr=Prime[Range[2000]]}, Select[Thread[{Rest[FoldList[ Times, 1, pr]], pr}], PrimeQ[ First[#]-1]&]]][[2]] (* From Harvey P. Dale, June 21 2011 *)
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CROSSREFS
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Cf. A057704, A057705, A002110, A005234, A014545, A018239.
Sequence in context: A105071 A089251 A147568 * A032457 A122564 A162876
Adjacent sequences: A006791 A006792 A006793 * A006795 A006796 A006797
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KEYWORD
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nonn,hard,more,nice
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Stated incorrectly in CRC Standard Mathematical Tables and Formulae, 30th ed., 1996, p. 101; corrected in 2nd printing.
Corrected by Arlin Anderson (starship1(AT)gmail.com), who reports that he and Don Robinson have checked this sequence through about 63000 digits without finding another term (Jul 04 2000).
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STATUS
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approved
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