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%I #77 Apr 01 2024 06:27:39
%S 1,75898,341112,356926,475856,1880370,2061748,2312092,2733014,2788032,
%T 2877652,2985036,3214654,3638450,4896418,5897794,6339004
%N Numbers k such that k^524288 + 1 is prime.
%C Numbers k such that k^(2^j) + 1 is a generalized Fermat prime for j=19.
%C 1880370 is a member, but its position is not yet known. - _Jeppe Stig Nielsen_, Jan 24 2018
%C PrimeGrid has now tested and double checked the necessary candidates to prove that 1880370 is a(6). - _Jeppe Stig Nielsen_, Feb 20 2018
%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 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 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-75898_524288.pdf">Announcement of n=75898</a>
%H PrimeGrid, <a href="http://www.primegrid.com/download/GFN-341112_524288.pdf">Announcement of n=341112</a>
%H PrimeGrid, <a href="http://www.primegrid.com/download/GFN-356926_524288.pdf">Announcement of n=356926</a>
%H PrimeGrid, <a href="http://www.primegrid.com/download/GFN-475856_524288.pdf">Announcement of n=475856</a>
%H PrimeGrid, <a href="http://www.primegrid.com/download/GFN-1880370_524288.pdf">Announcement of n=1880370</a>
%H PrimeGrid, <a href="http://www.primegrid.com/download/GFN-2061748_524288.pdf">Announcement of n=2061748</a>
%H PrimeGrid, <a href="http://www.primegrid.com/download/GFN-2312092_524288.pdf">Announcement of n=2312092</a>
%H PrimeGrid, <a href="http://www.primegrid.com/gfn_history.php">GFN Prime Search Status and History</a>
%H PrimeGrid, <a href="http://www.primegrid.com/primes/primes.php?project=GFN524288&factors=+&only=ALL&announcements=ALL&sortby=size&dc=no&search=">PrimeGrid Primes - (GFN524288) Generalized Fermat Prime Search n=524288</a>
%H The Prime Pages, <a href="https://t5k.org/primes/search.php?Description=%25%5E524288%2B1%24&Comment=generalized+Fermat&Number=99&Style=HTML">Database search results</a>
%o (PARI) is(n)=isprime(n^524288+1) \\ _Charles R Greathouse IV_, Feb 20 2017
%Y Cf. A056993, A005574, A000068, A006314, A006313, A006315, A006316, A056994, A056995, A057465, A057002, A088361, A088362, A226528, A226529, A226530, A251597, A253854, A244150, A321323.
%K nonn,hard,more
%O 1,2
%A _Felix Fröhlich_, Jun 16 2014
%E a(6) from _Jeppe Stig Nielsen_, Feb 20 2018
%E a(7) from _Jeppe Stig Nielsen_, Apr 27 2018
%E a(1) = 1 inserted and a(8) added by _Jeppe Stig Nielsen_, Sep 10 2018
%E a(9)-a(12) from _Jeppe Stig Nielsen_, Sep 21 2019
%E a(13) from _Jeppe Stig Nielsen_, Dec 27 2019
%E a(14) from _Ray Chandler_, Mar 28 2022
%E a(15)-a(17) communicated by _Jeppe Stig Nielsen_, Apr 01 2024
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