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

Author

Felix Fröhlich, Dec 05 2014

Keywords

• nonn

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

• Jeppe Stig Nielsen, Table of n, a(n) for n = 1..4048 (some previous contributions from Ray Chandler and Felix Fröhlich)
• 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.

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