A215058 Number of primes of the form 1 + b^128 for 1 < b < 10^n.

0, 0, 7, 25, 242, 1933, 16080, 139921, 1234958

Offset: 1

Author

Henryk Dabrowski, Aug 01 2012

Keywords

• nonn
• more

Comments

Primes 1 + b^128 are a form of generalized Fermat primes.

It is conjectured that a(n) is asymptotic to 0.0242888*li(10^n)

Examples

			a(3) = 7 because the generalized Fermat numbers F_7(b) where b<10^3 are prime only for b: 120, 190, 234, 506, 532, 548, 960.
		

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)

Crossrefs

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

Programs

PARI

a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^128+1))

Extensions

a(8)-a(9) from Kellen Shenton, Aug 10 2020