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A006794 Primes p such that -1 + product of primes up to p is prime.
(Formerly M2474)
19
3, 5, 11, 13, 41, 89, 317, 337, 991, 1873, 2053, 2377, 4093, 4297, 4583, 6569, 13033, 15877 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Or, p such that primorial(p) - 1 is prime.

a(19) > 287177.  This corresponds to primorial(prime(25000)) which has 124424 digits. - Robert Price, Nov 22 2014

REFERENCES

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.

Des MacHale, Infinitely many proofs that there are infinitely many primes, Math. Gazette, 97 (No. 540, 2013), 495-498.

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

LINKS

Table of n, a(n) for n=1..18.

C. K. Caldwell, Primorial Primes

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.

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

Eric Weisstein's World of Mathematics, Primorial

FORMULA

a(n) = A000040(A057704(n)).

MATHEMATICA

primorial[p_] := Product[Prime[k], {k, 1, PrimePi[p]}]; Select[Prime[Range[1900]], PrimeQ[primorial[#] - 1] &] (* Jean-Fran├žois Alcover, Mar 16 2011 *)

Transpose[With[{pr=Prime[Range[2000]]}, Select[Thread[{Rest[FoldList[ Times, 1, pr]], pr}], PrimeQ[ First[#]-1]&]]][[2]] (* Harvey P. Dale, Jun 21 2011 *)

CROSSREFS

Cf. A057704, A057705, A002110, A005234, A014545, A018239.

Sequence in context: A105071 A089251 A147568 * A032457 A122564 A162876

Adjacent sequences:  A006791 A006792 A006793 * A006795 A006796 A006797

KEYWORD

nonn,hard,more,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

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).

STATUS

approved

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Last modified December 21 11:25 EST 2014. Contains 252310 sequences.