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

1,3

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)

Links

Table of n, a(n) for n=1..9.

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)

Example

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.

Prog

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

Crossrefs

Cf. A215047, A215048, A215049, A215050, A215051, A215058.

Sequence in context: A187157 A332597 A331448 * A222400 A358884 A280159

Adjacent sequences: A215054 A215055 A215056 * A215058 A215059 A215060

Keyword

nonn,more

Author

Henryk Dabrowski, Aug 01 2012

Extensions

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

Status

approved