A215700 - OEIS

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A215700

Number of primes of the form 1 + b^1024 for 1 < b < 10^n.

4

0, 0, 1, 14, 81, 578

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OFFSET

1,4

COMMENTS

Primes 1 + b^1024 are a form of generalized Fermat primes.

It is conjectured that a(n) is asymptotic to 0.00783139*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) = 1 because the generalized Fermat numbers F_10(b) where b<10^3 are prime only for b = 824.

PROG

(PARI) a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^1024+1))

CROSSREFS

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

Sequence in context: A309338 A215472 A209942 * A199912 A082971 A374650

Adjacent sequences: A215697 A215698 A215699 * A215701 A215702 A215703

KEYWORD

nonn

AUTHOR

Henryk Dabrowski, Aug 21 2012

STATUS

approved