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• ## More sequences from Sloane's Encyclopedia: Based on Euclid's proof that there are infinitely many primes

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• %I A051342 %S A051342 3,7,31,211,2311,59,19,347,317,331,200560490131,181,61,167,953,73,277, %T A051342
Message 1 of 1 , Nov 1, 2003
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%I A051342
%S A051342 3,7,31,211,2311,59,19,347,317,331,200560490131,181,61,167,953,73,277,
%T A051342 223,54730729297,1063,2521,22093,265739,131,2336993,960703,2297,149,
%U A051342 334507,5122427,1543,1951,881,678279959005528882498681487,87549524399
%N A051342 Least prime divisor of 1 + (product of first n primes).
%C A051342 Based on Euclid's proof that there are infinitely many primes.
%H A051342 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha102.htm">Factorizations of many number sequences</a>
%H A051342 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha103.htm">Factorizations of many number sequences</a>
%H A051342 R. G. Wilson v, <a href="http://www.research.att.com/~njas/sequences/a38507.txt">Explicit factorizations</a>
%Y A051342 a(n) = A020639(1+A002110(n)). Cf. A014545.
%Y A051342 Sequence in context: A000644 A015459 A059296 this_sequence A002585 A073918 A083772
%Y A051342 Adjacent sequences: A051339 A051340 A051341 this_sequence A051343 A051344 A051345
%K A051342 nonn
%O A051342 1,1
%A A051342 Labos E. (labos(AT)ana1.sote.hu)

%I A002585 M2697 N1081
%S A002585 3,7,31,211,2311,509,277,27953,703763,34231,200560490131,676421,
%T A002585 11072701,78339888213593,13808181181,18564761860301,19026377261,
%U A002585 525956867082542470777,143581524529603,2892214489673,16156160491570418147806951,96888414202798247,1004988035964897329167431269
%N A002585 Largest prime factor of 2*3*5*7*11*13.... + 1.
%C A002585 Based on Euclid's proof that there are infinitely many primes.
%D A002585 A. Borning, Some results for k!+-1 and 2.3.5...p+-1, Math. Comp., 26 (1972), 567-570.
%D A002585 M. Kraitchik, On the divisibility of factorials, Scripta Math., 14 (1948), 24-26 (but beware errors).
%D A002585 M. Kraitchik, Introduction \`{a} la Th\'{e}orie des Nombres. Gauthier-Villars, Paris, 1952, p. 2.
%D A002585 S. Kravitz and D. E. Penney, An extension of Trigg's table, Math. Mag., 48 (1975), 92-96.
%H A002585 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha102.htm">Factorizations of many number sequences</a>
%H A002585 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha103.htm">Factorizations of many number sequences</a>
%H A002585 R. G. Wilson v, <a href="http://www.research.att.com/~njas/sequences/a38507.txt">Explicit factorizations</a>
%H A002585 E. W. Weisstein, <a href="http://mathworld.wolfram.com/EuclidNumber.html">Link to a section of The World of Mathematics.</a>
%Y A002585 Cf. A002584, A051342.
%Y A002585 Sequence in context: A015459 A059296 A051342 this_sequence A073918 A083772 A066676
%Y A002585 Adjacent sequences: A002582 A002583 A002584 this_sequence A002586 A002587 A002588
%K A002585 nonn,nice
%O A002585 1,1
%A A002585 njas
%E A002585 More terms from Labos E. (labos(AT)ana1.sote.hu), May 02 2000, and Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 24 2001

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Respectfully, Roger L. Bagula
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