

A215048


Number of primes of the form 1 + b^4 for 1 < b < 10^n.


13




OFFSET

1,1


COMMENTS

Primes 1 + b^4 are a form of generalized Fermat primes. It is conjectured that a(n) is asymptotic to 0.66974*li(10^n).


REFERENCES

Daniel Shanks, On Numbers of the Form n^4 + 1, Math. Comput. 15 (1961), 186189.


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)
Mersenne Wiki, Table of known GF primes b^n+1 where n (exponent) is at least 8192.


FORMULA

a(n) = A214452(4*n)  1.


EXAMPLE

a(1) = 3 because the only generalized Fermat primes F_2(b) where b<10^1 are the primes: 17, 257, 1297.


MATHEMATICA

Table[Length[Select[Range[2, 10^n1]^4 + 1, PrimeQ]], {n, 5}] (* T. D. Noe, Aug 02 2012 *)


PROG

(PARI) a(n) = sum(b=1, 10^n/21, isprime((2*b)^4+1))


CROSSREFS

Cf. A214452.
Sequence in context: A103730 A074556 A295808 * A119259 A249921 A174404
Adjacent sequences: A215045 A215046 A215047 * A215049 A215050 A215051


KEYWORD

nonn


AUTHOR

Henryk Dabrowski, Aug 01 2012


STATUS

approved



