A215961 Number of primes of the form 1 + b^8192 for 1 < b < 10^n.

0, 0, 0, 0, 3, 74, 621

Offset: 1

Author

Henryk Dabrowski, Aug 29 2012

Keywords

• nonn
• more

Comments

Primes 1 + b^8192 are a form of generalized Fermat primes. It is conjectured that a(n) is asymptotic to 0.00103368*li(10^n).

Examples

			a(5) = 3 because the generalized Fermat numbers F_13(b) where b<10^5 are prime only for b = 30406, 71852, 85654.
		

Links

• 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

Crossrefs

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

Programs

PARI

a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^8192+1))