A215698 Number of primes of the form 1 + b^256 for 1 < b < 10^n.

0, 0, 4, 30, 272, 2322

Offset

1,3

Comments

Primes 1 + b^256 are a form of generalized Fermat primes.

It is conjectured that a(n) is asymptotic to 0.0290422*li(10^n)

Links

Table of n, a(n) for n=1..6.

Yves Gallot, Status of the smallest base values yielding Generalized Fermat primes

Yves Gallot, How many prime numbers appear in a sequence ?

Yves Gallot, A Problem on the Conjecture Concerning the Distribution of Generalized Fermat Prime numbers (a new method for the search for large primes)

Example

a(3) = 4 because the generalized Fermat numbers F_8(b) where b<10^3 are prime only for b: 278, 614, 892, 898.

Prog

(PARI) a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^256+1))

Crossrefs

Cf. A215047, A215048, A215049, A215050, A215051, A215057, A215058.

Sequence in context: A052658 A340895 A220442 * A367872 A376326 A179540

Adjacent sequences: A215695 A215696 A215697 * A215699 A215700 A215701

Keyword

nonn

Author

Henryk Dabrowski, Aug 21 2012

Status

approved