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A215701 Number of primes of the form 1 + b^2048 for 1 < b < 10^n. 0
0, 0, 1, 4, 40, 276 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

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)

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

PROG

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

CROSSREFS

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

Sequence in context: A115286 A119635 A283660 * A212699 A061318 A277652

Adjacent sequences:  A215698 A215699 A215700 * A215702 A215703 A215704

KEYWORD

nonn

AUTHOR

Henryk Dabrowski, Aug 21 2012

STATUS

approved

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Last modified November 21 16:04 EST 2019. Contains 329371 sequences. (Running on oeis4.)