A215057 Number of primes of the form 1 + b^64 for 1 < b < 10^n.

0, 0, 8, 92, 606, 4835, 41059, 354239, 3133668

Offset: 1

Author

Henryk Dabrowski, Aug 01 2012

Keywords

• nonn
• more

Comments

Primes 1 + b^64 are a form of generalized Fermat primes.

It is conjectured that a(n) is asymptotic to 0.0616053*li(10^n)

Examples

			a(3) = 8 because the Fermat numbers F_6(b) where b<10^3 are prime only for b = 102, 162, 274, 300, 412, 562, 592, 728.
		

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, A215058.

Programs

PARI

a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^64+1))

Extensions

a(8)-a(9) from Kellen Shenton, Aug 09 2020