A214452 Number of primes of the form x^4 + 1 less than 10^n.

1, 2, 3, 4, 5, 8, 13, 18, 27, 45, 70, 111, 180, 308, 491, 790, 1319, 2231, 3747, 6396, 10761, 18291, 30947, 52611, 89157, 152514, 260277, 445869, 762919, 1307688, 2246172, 3857544, 6641424, 11440114, 19728780, 34057328, 58834623, 101709014, 176009032, 304766442

Offset: 1

Author

Henryk Dabrowski, Jul 18 2012

Keywords

• nonn

Comments

It is conjectured that there are infinitely many primes of the form x^4 + 1 (and thus this sequence never becomes constant), but this has not been proved.

Examples

			a(3) = 3 because the only primes of the form x^4 + 1 < 10^3 are the primes: 2, 17, 257.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..46

Crossrefs

Cf. A083844, A214454, A214455.

Programs

PARI

a(n) = sum(k=1,(10^n-1)^(1/4), isprime(k^4+1))

Extensions

More terms from Henryk Dabrowski, Jul 26 2012

a(37)-a(40) from Chai Wah Wu, Oct 13 2018