A253854 Numbers b such that b^131072 + 1 is prime.

1, 62722, 130816, 228188, 386892, 572186, 689186, 909548, 1063730, 1176694, 1361244, 1372930, 1560730, 1660830, 1717162, 1722230, 1766192, 1955556, 2194180, 2280466, 2639850, 3450080, 3615210, 3814944, 4085818, 4329134, 4893072, 4974408, 5326454, 5400728, 5471814

Offset

1,2

Comments

Base values b yielding a generalized Fermat prime b^(2^k)+1 for k=17.

The first member exceeding 10^((10^6-1)/2^17) is known to be 42654182. - Jeppe Stig Nielsen, Jan 30 2016

Links

Jeppe Stig Nielsen, Table of n, a(n) for n = 1..515 (from a massive computation by PrimeGrid).

C. K. Caldwell, 1560730^131072+1, The Largest Known Primes

C. K. Caldwell, Search result %^131072+1.

J. S. S. Nielsen, Generalized Fermat Primes sorted by base (see table at the bottom of the page)

PrimeGrid, PrimeGrid Primes - (GFN131072) Generalized Fermat Prime Search n=131072

PrimeGrid, Generalized Fermat statistics

Crossrefs

Cf. A056993, A005574, A000068, A006314, A006313, A006315, A006316, A056994, A056995, A057465, A057002, A088361, A088362, A226528, A226529, A226530, A251597, A244150, A243959, A321323.

Sequence in context: A205764 A209207 A224649 * A237675 A135430 A049025

Adjacent sequences: A253851 A253852 A253853 * A253855 A253856 A253857

Keyword

nonn,hard

Author

Felix Fröhlich, Jan 17 2015

Extensions

Missing term a(8) inserted by Jeppe Stig Nielsen, Jul 02 2015

a(13) from Felix Fröhlich, Nov 01 2015

a(14)-a(20) from Jeppe Stig Nielsen, Jan 30 2016

a(21)-a(31) from Jeppe Stig Nielsen, Sep 06 2017

a(1) = 1 inserted by Jeppe Stig Nielsen, Sep 10 2018

Status

approved