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

0,1

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

Links

Table of n, a(n) for n=0..13.

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).

Example

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

Mathematica

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

Crossrefs

Cf. A056993, A001359.

Sequence in context: A366628 A320305 A064025 * A273875 A054709 A121806

Adjacent sequences: A182151 A182152 A182153 * A182155 A182156 A182157

Keyword

nonn,more,hard

Author

Manuel Valdivia, Apr 15 2012

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

Status

approved