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Search: id:A002585
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| A002585 |
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Largest prime factor of 1 + (product of first n primes).
(Formerly M2697 N1081)
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+0
10
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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Based on Euclid's proof that there are infinitely many primes.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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).
M. Kraitchik, Introduction \`{a} la Th\'{e}orie des Nombres. Gauthier-Villars, Paris, 1952, p. 2.
S. Kravitz and D. E. Penney, An extension of Trigg's table, Math. Mag., 48 (1975), 92-96.
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LINKS
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Hisanori Mishima, Factorizations of many number sequences
Hisanori Mishima, Factorizations of many number sequences
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
R. G. Wilson v, Explicit factorizations
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CROSSREFS
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Cf. A002584, A051342.
Sequence in context: A059296 A123332 A051342 this_sequence A103785 A083772 A093441
Adjacent sequences: A002582 A002583 A002584 this_sequence A002586 A002587 A002588
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Labos E. (labos(AT)ana.sote.hu), May 02 2000 and Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 24 2001
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