%I #83 Apr 03 2023 10:36:13
%S 1,24518,40734,145310,361658,525094,676754,773620,1415198,1488256,
%T 1615588,1828858,2042774,2514168,2611294,2676404,3060772,3547726,
%U 3596074,3673932,3853792,3933508,4246258,4489246,5152128,5205422,5828034,6287774,6291332,8521794
%N Numbers b such that b^262144+1 is prime.
%C Base values b yielding a generalized Fermat prime b^(2^k)+1 for k=18.
%H Jeppe Stig Nielsen, <a href="/A244150/b244150.txt">Table of n, a(n) for n = 1..53</a>
%H C. Caldwell, <a href="https://t5k.org/primes/lists/short.pdf">The largest known primes (Primes with 600,000 or more digits)</a>
%H C. Caldwell, <a href="https://primes.utm.edu/primes/search.php?Description=%25%5E262144%2B1%24&OnList=all&Number=200&Style=Text">The Prime Pages Database Search Output</a>
%H H. Dubner and Y. Gallot, <a href="http://dx.doi.org/10.1090/S0025-5718-01-01350-3">Distribution of generalized Fermat prime numbers</a>, Math. Comp., 71 (2002), 825-832.
%H M. Goetz, <a href="http://www.primegrid.com/forum_thread.php?id=6502">GFN Prime Discoveries</a>, PrimeGrid forum.
%H J. S. S. Nielsen, <a href="http://jeppesn.dk/generalized-fermat.html">Generalized Fermat Primes sorted by base</a> (See table at the bottom of the page.)
%H PrimeGrid, <a href="http://www.primegrid.com/download/gfn-40734_262144.pdf">Announcement of b=40734</a>
%H PrimeGrid, <a href="http://www.primegrid.com/download/gfn-145310_262144.pdf">Announcement of b=145310</a>
%H PrimeGrid, <a href="http://www.primegrid.com/download/gfn-361658_262144.pdf">Announcement of b=361658</a>
%H PrimeGrid, <a href="http://www.primegrid.com/download/gfn-525094_262144.pdf">Announcement of b=525094</a>
%H PrimeGrid, <a href="http://www.primegrid.com/download/gfn-676754_262144.pdf">Announcement of b=676754</a>
%H PrimeGrid, <a href="http://www.primegrid.com/download/gfn-773620_262144.pdf">Announcement of b=773620</a>
%H PrimeGrid, <a href="http://www.primegrid.com/download/GFN-1415198_262144.pdf">Announcement of b=1415198</a>
%H PrimeGrid, <a href="http://www.primegrid.com/download/GFN-1488256_262144.pdf">Announcement of b=1488256</a>
%H PrimeGrid, <a href="http://www.primegrid.com/download/GFN-1615588_262144.pdf">Announcement of b=1615588</a>
%H PrimeGrid, <a href="http://www.primegrid.com/download/GFN-1828858_262144.pdf">Announcement of b=1828858</a>
%H PrimeGrid, <a href="http://www.primegrid.com/download/GFN-2042774_262144.pdf">Announcement of b=2042774</a>
%H PrimeGrid, <a href="http://www.primegrid.com/primes/primes.php?project=GFN262144&factors=+&only=ALL&announcements=ALL&sortby=size&dc=no&search=">PrimeGrid Primes - (GFN262144) Generalized Fermat Prime Search n=262144</a>
%H PrimePages, <a href="https://primes.utm.edu/primes/page.php?id=121375">1488256^262144 + 1</a>
%H PrimePages, <a href="https://primes.utm.edu/primes/page.php?id=121619">1615588^262144 + 1</a>
%Y Cf. A056993, A005574, A000068, A006314, A006313, A006315, A006316, A056994, A056995, A057465, A057002, A088361, A088362, A226528, A226529, A226530, A251597, A253854, A243959, A321323.
%K nonn,hard
%O 1,2
%A _Felix Fröhlich_, Jun 21 2014
%E a(9), announced in message 92163 in PrimeGrid forum, added by _Felix Fröhlich_, Feb 17 2016
%E a(10), a(11) sent by Maximilian Pacher, Jun 27 2016, and a(12) on Aug 24 2016. - _N. J. A. Sloane_
%E a(13) from _Felix Fröhlich_, Nov 27 2016
%E a(14)-a(17) from _Jeppe Stig Nielsen_, Sep 06 2017
%E a(1) = 1 inserted by and more terms from _Jeppe Stig Nielsen_, Sep 10 2018
%E a(27)-a(30) from _Jeppe Stig Nielsen_, Sep 21 2019