

A243959


Numbers k such that k^524288 + 1 is prime.


22



1, 75898, 341112, 356926, 475856, 1880370, 2061748, 2312092, 2733014, 2788032, 2877652, 2985036, 3214654
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OFFSET

1,2


COMMENTS

Numbers k such that k^(2^j) + 1 is a generalized Fermat prime for j=19.
1880370 is a member, but its position is not yet known.  Jeppe Stig Nielsen, Jan 24 2018
PrimeGrid has now tested and double checked the necessary candidates to prove that 1880370 is a(6).  Jeppe Stig Nielsen, Feb 20 2018


LINKS

Table of n, a(n) for n=1..13.
C. Caldwell, The largest known primes (Primes with 600,000 or more digits)
H. Dubner and Y. Gallot, Distribution of generalized Fermat prime numbers, Math. Comp., 71 (2002), 825832.
J. S. S. Nielsen, Generalized Fermat Primes sorted by base (See table at the bottom of the page.)
PrimeGrid, Announcement of n=75898
PrimeGrid, Announcement of n=341112
PrimeGrid, Announcement of n=356926
PrimeGrid, Announcement of n=475856
PrimeGrid, Announcement of n=1880370
PrimeGrid, Announcement of n=2061748
PrimeGrid, Announcement of n=2312092
PrimeGrid, GFN Prime Search Status and History
PrimeGrid, PrimeGrid Primes  (GFN524288) Generalized Fermat Prime Search n=524288


PROG

(PARI) is(n)=isprime(n^524288+1) \\ Charles R Greathouse IV, Feb 20 2017


CROSSREFS

Cf. A056993, A005574, A000068, A006314, A006313, A006315, A006316, A056994, A056995, A057465, A057002, A088361, A088362, A226528, A226529, A226530, A251597, A253854, A244150, A321323.
Sequence in context: A323025 A323804 A135209 * A236807 A251470 A091294
Adjacent sequences: A243956 A243957 A243958 * A243960 A243961 A243962


KEYWORD

nonn,hard,more


AUTHOR

Felix FrÃ¶hlich, Jun 16 2014


EXTENSIONS

a(6) from Jeppe Stig Nielsen, Feb 20 2018
a(7) from Jeppe Stig Nielsen, Apr 27 2018
a(1) = 1 inserted and a(8) added by Jeppe Stig Nielsen, Sep 10 2018
a(9)a(12) from Jeppe Stig Nielsen, Sep 21 2019
a(13) from Jeppe Stig Nielsen, Dec 27 2019


STATUS

approved



