A215702 Number of primes of the form 1 + b^4096 for 1 < b < 10^n.

0, 0, 0, 2, 16, 170

Offset

1,4

Comments

Primes 1 + b^4096 are a form of generalized Fermat primes.

It is conjectured that a(n) is asymptotic to 0.00205697*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(4) = 2 because the generalized Fermat numbers F_12(b) where b<10^4 are prime only for b = 1534, 7316.

Prog

(PARI) a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^4096+1))

Crossrefs

Cf. A215047, A215048, A215049, A215050, A215051, A215057, A215058, A215698.

Sequence in context: A217799 A123555 A219446 * A155659 A108999 A355408

Adjacent sequences: A215699 A215700 A215701 * A215703 A215704 A215705

Keyword

nonn

Author

Henryk Dabrowski, Aug 21 2012

Status

approved