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 A002585 Largest prime factor of 1 + (product of first n primes). (Formerly M2697 N1081) 10
 3, 7, 31, 211, 2311, 509, 277, 27953, 703763, 34231, 200560490131, 676421, 11072701, 78339888213593, 13808181181, 18564761860301, 19026377261, 525956867082542470777, 143581524529603, 2892214489673, 16156160491570418147806951, 96888414202798247, 1004988035964897329167431269 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Based on Euclid's proof that there are infinitely many primes. The products of the first primes are called primorial numbers. - Franklin T. Adams-Watters, Jun 12 2014 REFERENCES M. Kraitchik, On the divisibility of factorials, Scripta Math., 14 (1948), 24-26 (but beware errors). M. Kraitchik, Introduction à la Théorie des Nombres. Gauthier-Villars, Paris, 1952, p. 2. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Sean A. Irvine and Amiram Eldar, Table of n, a(n) for n = 1..87 (terms 1..81 from Sean A. Irvine) A. Borning, Some results for k!+-1 and 2.3.5...p+-1, Math. Comp., 26 (1972), 567-570. M. Kraitchik, On the divisibility of factorials, Scripta Math., 14 (1948), 24-26 (but beware errors). [Annotated scanned copy] S. Kravitz and D. E. Penney, An extension of Trigg's table, Math. Mag., 48 (1975), 92-96. S. Kravitz and D. E. Penney, An extension of Trigg's table, Math. Mag., 48 (1975), 92-96. [Annotated scanned copy; also letter from N. J. A. Sloane to John Selfridge] 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 [math.HO], 2012-2018. - From N. J. A. Sloane, Jun 13 2012 Hisanori Mishima, Factorizations of many number sequences Hisanori Mishima, Factorizations of many number sequences John Selfridge, Marvin Wunderlich, Robert Morris, N. J. A. Sloane, Correspondence, 1975 Eric Weisstein's World of Mathematics, Euclid Number. R. G. Wilson v, Explicit factorizations FORMULA a(n) = A006530(A006862(n)). - Amiram Eldar, Feb 13 2020 MATHEMATICA FactorInteger[#][[-1, 1]]&/@Rest[FoldList[Times, 1, Prime[Range[30]]]+1] (* Harvey P. Dale, Apr 10 2012 *) PROG (PARI) a(n)=my(f=factor(prod(i=1, n, prime(i))+1)[, 1]); f[#f] \\ Charles R Greathouse IV, Feb 07 2017 CROSSREFS Cf. A002110, A002584, A006530, A006862, A051342. Sequence in context: A059296 A123332 A051342 * A103785 A289127 A289125 Adjacent sequences:  A002582 A002583 A002584 * A002586 A002587 A002588 KEYWORD nonn,nice AUTHOR EXTENSIONS More terms from Labos Elemer, May 02 2000 More terms from Robert G. Wilson v, Mar 24 2001 STATUS approved

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Last modified January 27 17:59 EST 2021. Contains 340470 sequences. (Running on oeis4.)