A215969 Number of primes of the form 1 + b^32768 for 1 < b < 10^n.

0, 0, 0, 0, 1, 16, 64

Offset

1,6

Comments

Primes 1 + b^32768 are a form of generalized Fermat primes.

It is conjectured that a(n) is asymptotic to 0.000177083*li(10^n)

Links

Table of n, a(n) for n=1..7.

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)

Mersenne Wiki, Table of known GF primes b^n+1 where n (exponent) is at least 8192

Example

a(5) = 1 because the generalized Fermat numbers F_15(b) where b<10^5 are prime only for b = 70906.

Prog

(PARI) a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^32768 + 1))

Crossrefs

Cf. A215047, A215048, A215049, A215050, A215051, A215057, A215058, A215698, A215699, A215700.

Sequence in context: A100176 A060091 A076751 * A333663 A155985 A211222

Adjacent sequences: A215966 A215967 A215968 * A215970 A215971 A215972

Keyword

nonn

Author

Henryk Dabrowski, Aug 29 2012

Status

approved