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

Author

Felix Fröhlich, Jan 17 2015

Keywords

• nonn
• hard

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..1243
• 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.

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