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A215058 Number of primes of the form 1 + b^128 for 1 < b < 10^n. 11
0, 0, 7, 25, 242, 1933, 16080, 139921, 1234958 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Primes 1 + b^128 are a form of generalized Fermat primes.

It is conjectured that a(n) is asymptotic to 0.0242888*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) = 7 because the generalized Fermat numbers F_7(b) where b<10^3 are prime only for b: 120, 190, 234, 506, 532, 548, 960.

PROG

(PARI) a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^128+1))

CROSSREFS

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

Sequence in context: A293532 A208823 A197913 * A214538 A290882 A197651

Adjacent sequences:  A215055 A215056 A215057 * A215059 A215060 A215061

KEYWORD

nonn,more

AUTHOR

Henryk Dabrowski, Aug 01 2012

EXTENSIONS

a(8)-a(9) from Kellen Shenton, Aug 10 2020

STATUS

approved

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Last modified June 22 10:56 EDT 2021. Contains 345375 sequences. (Running on oeis4.)