A243959 Numbers k such that k^524288 + 1 is prime.

1, 75898, 341112, 356926, 475856, 1880370, 2061748, 2312092, 2733014, 2788032, 2877652, 2985036, 3214654, 3638450, 4896418, 5897794, 6339004

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..17.

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), 825-832.

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

The Prime Pages, Database search results

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 Fröhlich, 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

a(14) from Ray Chandler, Mar 28 2022

a(15)-a(17) communicated by Jeppe Stig Nielsen, Apr 01 2024

Status

approved