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A215702 Number of primes of the form 1 + b^4096 for 1 < b < 10^n. 0
0, 0, 0, 2, 16, 170 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Primes 1 + b^4096 are a form of generalized Fermat primes.

It is conjectured that a(n) is asymptotic to 0.00205697*li(10^n)

LINKS

Table of n, a(n) for n=1..6.

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(4) = 2 because the generalized Fermat numbers F_12(b) where b<10^4 are prime only for b = 1534, 7316.

PROG

(PARI) a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^4096+1))

CROSSREFS

Cf. A215047, A215048, A215049, A215050, A215051, A215057, A215058, A215698.

Sequence in context: A217799 A123555 A219446 * A155659 A108999 A138014

Adjacent sequences:  A215699 A215700 A215701 * A215703 A215704 A215705

KEYWORD

nonn

AUTHOR

Henryk Dabrowski, Aug 21 2012

STATUS

approved

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Last modified September 23 22:32 EDT 2020. Contains 337315 sequences. (Running on oeis4.)