|
%I #35 Aug 25 2014 11:25:04
%S 293,439,547,1093,1171,2341,3511
%N Wieferich prime candidates: primes of the form A242139(n)+1 also having the form {m*(2^rs - 1)/(2^r - 1)}+1.
%C 292 = 100100100, 438 = 110110110, 546 = 001000100010, 1092 = 010001000100, 1170 = 010010010010, 2340 = 100100100100, 3510 = 110110110110.
%C According to Dobson, all primes where m is of the form 2*(4^(r/2)-1)/3 cannot be Wieferich primes.
%C Triples (m, r, s) producing the terms through the formula in definition are (4, 3, 3), (6, 3, 3), (2, 4, 3), (4, 4, 3), (2, 3, 4), (4, 3, 4), (6, 3, 4).
%H S. Agou, <a href="http://www.digizeitschriften.de/dms/resolveppn/?PPN=GDZPPN00219368X">Irréductibilité des polynômes f(X^p^r-aX) sur un corps fini F_p^s</a>, J. reine angew. Mat. 292 (1977), 191-195.
%H J. B. Dobson, <a href="http://web.archive.org/web/20110828180453/http://library.uwinnipeg.ca/people/dobson/mathematics/Wieferich_primes.html">A note on the two known Wieferich primes</a> (Archive of the site from August 28 2011)
%Y Cf. A001220, A242139.
%K nonn,more
%O 1,1
%A _Felix Fröhlich_, Jul 26 2014
|
