A182154 Smallest k >= 2 such that k^(2^n)+1 is the lesser member of a twin prime pair.

2, 2, 2, 4, 2, 49592, 7132, 532, 333482, 2226686, 3543554, 23379038, 1249625230, 188489906

Offset: 0

Author

Manuel Valdivia, Apr 15 2012

Keywords

• nonn
• more
• hard

Comments

These lesser of twin prime pairs are also generalized Fermat primes, (not possible for greater of twin prime pairs, except for 5).

When extending this sequence, it is useful if the primes b^(2^n)+1 are known in advance (Gallot link). - Jeppe Stig Nielsen, Sep 25 2019

For later terms, the bigger twin is only a probable prime, not a proven prime. - Jeppe Stig Nielsen, Nov 24 2022

Examples

			2^(2^4)+1 = 65537 = A001359(861), then a(4) = 2.
		

Links

• Yves Gallot, Generalized Fermat Prime Search.
• OEIS Wiki, Generalized Fermat numbers.
• PrimeGrid and "Stream", GFN-1x Small Primes search, mentions a(12) and a(13).

Crossrefs

Cf. A056993, A001359.

Programs

Mathematica

Table[k=2; While[!PrimeQ[k^(2^n)+1]||!PrimeQ[k^(2^n)+3],k++]; k,{n,0,7}]

Extensions

a(8)-a(10) from Jeppe Stig Nielsen, Sep 25 2019

Name edited by Felix Fröhlich, Sep 25 2019

a(11)-a(13) from Jeppe Stig Nielsen, Nov 24 2022