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, 8630170, 9332124, 10913140, 11937916

Offset: 1

Author

Felix Fröhlich, Jun 16 2014

Keywords

• nonn
• hard
• more

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

• 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

Crossrefs

Cf. A056993, A005574, A000068, A006314, A006313, A006315, A006316, A056994, A056995, A057465, A057002, A088361, A088362, A226528, A226529, A226530, A251597, A253854, A244150, A321323.

Programs

PARI

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

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

a(18)-a(21) from Jeppe Stig Nielsen, Jan 11 2025