A215701 Number of primes of the form 1 + b^2048 for 1 < b < 10^n.

0, 0, 1, 4, 40, 276

Offset: 1

Author

Henryk Dabrowski, Aug 21 2012

Keywords

• nonn

Comments

Primes 1 + b^2048 are a form of generalized Fermat primes.

It is conjectured that a(n) is asymptotic to 0.00352764*li(10^n)

Examples

			a(4) = 4 because the generalized Fermat numbers F_11(b) where b<10^4 are prime only for b = 150, 2558, 4650, 4772.
		

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, A215058, A215698.

Programs

PARI

a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^2048+1))