A251597 Numbers b such that b^65536 + 1 is prime.

1, 48594, 108368, 141146, 189590, 255694, 291726, 292550, 357868, 440846, 544118, 549868, 671600, 843832, 857678, 1024390, 1057476, 1087540, 1266062, 1361846, 1374038, 1478036, 1483076, 1540550, 1828502, 1874512, 1927034, 1966374, 2019300, 2041898, 2056292

Offset

1,2

Comments

Base values b yielding a generalized Fermat prime b^(2^k) + 1 for k=16.

First square member of sequence is 3934049284 = (A253854(1))^2. - Jeppe Stig Nielsen, Jun 29 2015

Links

Ray Chandler, Table of n, a(n) for n = 1..1604 (2..70 from Felix Fröhlich, 71..425 from Jeppe Stig Nielsen)

C. K. Caldwell, The Prime Database, Search Output.

Y. Gallot, Generalized Fermat Prime Search

Merfighters, Table of known GF primes b^n+1 where n(exponent) is at least 8192, Mersenne Wiki

J. S. S. Nielsen, Generalized Fermat Primes sorted by base (see table at the bottom of the page)

PrimeGrid, GFN Status by n-Range, Message 89145

Crossrefs

Cf. A056993, A005574, A000068, A006314, A006313, A006315, A006316, A056994, A056995, A057465, A057002, A088361, A088362, A226528, A226529, A226530, A253854, A244150, A243959, A321323.

Sequence in context: A278020 A237105 A234230 * A228676 A268852 A024753

Adjacent sequences: A251594 A251595 A251596 * A251598 A251599 A251600

Keyword

nonn

Author

Felix Fröhlich, Dec 05 2014

Extensions

Corrected last term, and extended, by Jeppe Stig Nielsen, Jun 29 2015

New b-file, updated with data from Message 89145 at PrimeGrid forum uploaded and sequence data corrected, by Felix Fröhlich, Jan 03 2016

a(1) = 1 inserted and new b-file by Jeppe Stig Nielsen, Sep 10 2018

Status

approved