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A215051 Number of primes of the form 1 + b^32 for 1 < b < 10^n. 12
0, 3, 22, 146, 1062, 8963, 74951, 651537, 5740807, 51389252 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 30 04:47 EDT 2021. Contains 346348 sequences. (Running on oeis4.)