A118539 Adjacent generalized Fermat primes.

3, 3, 3, 75, 113, 2163, 63739, 13221, 54809, 3656571, 6992033, 125441, 103859115, 56414915, 87888967

Offset: 1

Author

David Broadhurst, May 06 2006

Keywords

• hard
• more
• nonn

Comments

a(15)=87888967 but a(14) is unknown. - Jeppe Stig Nielsen, Mar 17 2018

The prime pair related to a(14) was found four days ago, and today double checking has proved that they are indeed the first occurrence for n=14. - Jeppe Stig Nielsen, May 02 2018

Examples

			a(11)=6992033 because 6992034^2048+1 is prime, 6992032^2048+1 is prime and no smaller pair of bases differing by 2 gives a pair of primes with the exponent 2^11=2048.
		

Links

• David Broadhurst, Posting to PrimeForm list.
• David Broadhurst, Chris Caldwell and others, GFN near mid-air collision, digest of 16 messages in primeform Yahoo group, May 2 - May 5, 2006. [Cached copy]
• Yves Gallot's compilation of generalized Fermat primes.

Crossrefs

Cf. A217993.

Formula

a(n) is the smallest number such that (a(n)+1)^(2^n)+1 and (a(n)-1)^(2^n)+1 are both prime.

a(n) = A217993(n) + 1. - Jeppe Stig Nielsen, Feb 27 2016

Extensions

a(13) from Jeppe Stig Nielsen, Mar 17 2018

a(14) and a(15) from Jeppe Stig Nielsen, May 02 2018