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 A051342 Smallest prime factor of 1 + (product of first n primes). 9
 3, 7, 31, 211, 2311, 59, 19, 347, 317, 331, 200560490131, 181, 61, 167, 953, 73, 277, 223, 54730729297, 1063, 2521, 22093, 265739, 131, 2336993, 960703, 2297, 149, 334507, 5122427, 1543, 1951, 881, 678279959005528882498681487, 87549524399, 23269086799180847 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Based on Euclid's proof that there are infinitely many primes. LINKS Amiram Eldar, Table of n, a(n) for n = 1..87 M. Kraitchik, On the divisibility of factorials, Scripta Math., 14 (1948), 24-26 (but beware errors). [Annotated scanned copy] Hisanori Mishima, Factorizations of many number sequences Hisanori Mishima, Factorizations of many number sequences R. G. Wilson v, Explicit factorizations FORMULA a(n) = A020639(1+A002110(n)). MAPLE a:= proc(n) local N, F, i;   N:= 1 + mul(ithprime(i), i=1..n);   F:= select(type, map(t->t[1], ifactors(N, easy)[2]), integer); if nops(F) >= 1 then return min(F) fi;   min(map(t->t[1], ifactors(N)[2])) end proc: seq(a(n), n=1..40); # Robert Israel, Oct 19 2014 MATHEMATICA Map[FactorInteger,    Table[Product[Prime[n], {n, 1, m}] + 1, {m, 1, 36}]][[All, 1]][[All, 1]] (* Geoffrey Critzer, Oct 19 2014 *) PROG (PARI) a(n) = factor(1 + prod(i=1, n, prime(i)))[1, 1]; \\ Michel Marcus, Dec 10 2013 CROSSREFS Cf. A014545, A002585. Sequence in context: A141385 A059296 A123332 * A002585 A103785 A289127 Adjacent sequences:  A051339 A051340 A051341 * A051343 A051344 A051345 KEYWORD nonn,changed AUTHOR EXTENSIONS One more term from Michel Marcus, Dec 10 2013 STATUS approved

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Last modified October 18 00:21 EDT 2019. Contains 328135 sequences. (Running on oeis4.)