

A215701


Number of primes of the form 1 + b^2048 for 1 < b < 10^n.


0




OFFSET

1,4


COMMENTS

Primes 1 + b^2048 are a form of generalized Fermat primes.
It is conjectured that a(n) is asymptotic to 0.00352764*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) = 4 because the generalized Fermat numbers F_11(b) where b<10^4 are prime only for b = 150, 2558, 4650, 4772.


PROG

(PARI) a(n) = sum(b=1, 10^n/21, isprime((2*b)^2048+1))


CROSSREFS

Cf. A215047, A215048, A215049, A215050, A215051, A215057, A215058, A215698.
Sequence in context: A115286 A119635 A283660 * A212699 A061318 A277652
Adjacent sequences: A215698 A215699 A215700 * A215702 A215703 A215704


KEYWORD

nonn


AUTHOR

Henryk Dabrowski, Aug 21 2012


STATUS

approved



