Search: id:A152156 Results 1-1 of 1 results found. %I A152156 %S A152156 1,0,1,1,1,810129131,1220845804166146754, %T A152156 6964187975677595099156927503004398881, %U A152156 14553806122642016769237504145596730952769427034161327480375008633175279343120 %V A152156 -1,0,-1,-1,-1,-810129131,-1220845804166146754, %W A152156 6964187975677595099156927503004398881, %X A152156 14553806122642016769237504145596730952769427034161327480375008633175279343120 %N A152156 Minimal residues of Pepin's Test for Fermat Numbers using either 5 or 10 for the base. %C A152156 For n=0 or n>=2 the Fermat Number F(n) is prime if and only if 5^((F(n) - 1)/2) is congruent to -1 (mod F(n)). %C A152156 5 was the base originally used by Pepin. The base 10 gives the same results. %C A152156 Any positive integer k for which the Jacobi symbol (k|F(n)) is -1 can be used as the base instead. %D A152156 M. Krizek, F. Luca & L. Somer, 17 Lectures on Fermat Numbers, Springer-Verlag NY 2001, pp. 42-43. %H A152156 Dennis Martin, Table of n, a(n) for n = 0..11 %H A152156 Chris Caldwell, The Prime Pages: Pepin's Test. %H A152156 M. Krizek, F. Luca & L. Somer, 17 Lectures on Fermat Numbers, pp. 42-43. %F A152156 a(n) = 5^((F(n) - 1)/2) (mod F(n)), where F(n) is the n-th Fermat Number %e A152156 a(4) = 5^(32768) (mod 65537) = 65536 = -1 (mod F(4)), therefore F(4) is prime. %e A152156 a(5) = 5^(2147483648) (mod 4294967297) = -810129131 (mod F(5)), therefore F(5) is composite. %Y A152156 Cf. A000215, A019434, A152153, A152154, A152155 %Y A152156 Sequence in context: A166227 A104829 A166072 this_sequence A017540 A132216 A091340 %Y A152156 Adjacent sequences: A152153 A152154 A152155 this_sequence A152157 A152158 A152159 %K A152156 sign %O A152156 0,6 %A A152156 Dennis Martin (dennis.martin(AT)dptechnology.com), Nov 27 2008 Search completed in 0.001 seconds