

A215047


Number of primes of the form 1 + b^2 for 1 < b < 10^n.


14



3, 18, 111, 840, 6655, 54109, 456361, 3954180, 34900212, 312357933, 2826683629, 25814570671, 237542444179, 2199894223891
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OFFSET

1,1


COMMENTS

Primes 1 + b^2 are a form of generalized Fermat primes.
It is conjectured that a(n) is asymptotic to 0.6864067*li(10^n).


LINKS

Table of n, a(n) for n=1..14.
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)
Mersenne Wiki, Table of known GF primes b^n+1 where n (exponent) is at least 8192.
Daniel Shanks, On the Conjecture of Hardy & Littlewood concerning the Number of Primes of the Form n^2 + a, Math. Comp. 14 (1960), 320332.


FORMULA

a(n) = A083844(2*n)  1.


EXAMPLE

a(1) = 3 because the only generalized Fermat primes F_1(b) where b < 10^1 are the primes: 5, 17, 37.


MATHEMATICA

Table[Length[Select[Range[2, 10^n1]^2 + 1, PrimeQ]], {n, 5}] (* T. D. Noe, Aug 02 2012 *)


PROG

(PARI) a(n) = sum(b=1, 10^n/21, isprime((2*b)^2+1))


CROSSREFS

Cf. A083844, A206709.
Sequence in context: A000274 A207321 A193236 * A346578 A213099 A199259
Adjacent sequences: A215044 A215045 A215046 * A215048 A215049 A215050


KEYWORD

nonn,more


AUTHOR

Henryk Dabrowski, Aug 01 2012


EXTENSIONS

a(13)a(14) from Jinyuan Wang, Feb 23 2020


STATUS

approved



