A215051 Number of primes of the form 1 + b^32 for 1 < b < 10^n.

0, 3, 22, 146, 1062, 8963, 74951, 651537, 5740807, 51389252

Offset

1,2

Comments

Primes 1 + b^32 are a form of generalized Fermat primes.

It is conjectured that a(n) is asymptotic to 0.112903*li(10^n).

Links

Table of n, a(n) for n=1..10.

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)

Formula

a(n) = A214956(32*n) - 1.

Example

a(2) = 3 because the Fermat numbers F_5(b) where b<10^2 are prime only for b = 30, 54, 96.

Mathematica

Table[Length[Select[Range[2, 10^n-1]^32 + 1, PrimeQ]], {n, 4}] (* T. D. Noe, Aug 01 2012 *)

Prog

(PARI) a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^32+1))

Crossrefs

Cf. A214956, A215047, A215048, A215049, A215050, A215057, A215058

Sequence in context: A091636 A321003 A339227 * A156089 A110469 A121723

Adjacent sequences: A215048 A215049 A215050 * A215052 A215053 A215054

Keyword

nonn,more

Author

Henryk Dabrowski, Aug 01 2012

Extensions

a(9)-a(10) from Chai Wah Wu, Oct 18 2018

Status

approved