A256777 Primes of form n^2 + 625.

641, 661, 769, 821, 881, 1109, 1201, 1301, 1409, 2069, 2389, 2741, 3329, 3541, 3761, 3989, 4721, 6101, 6709, 7349, 7681, 8369, 9461, 12289, 14081, 14549, 16001, 18049, 19121, 20789, 25589, 28181, 31601, 32309, 33749, 35221, 35969, 37489, 38261, 39041, 39829

Offset: 1

Author

Reinhard Zumkeller, Apr 11 2015

Keywords

• nonn
• changed

Comments

Conjecture: sequence is infinite.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A010051, A000290; subsequence of A028916.

Primes of form n^2+b^4, b fixed: A002496 (b=1), A243451 (b=2), A256775 (b=3), A256776 (b=4), A256834 (b=6), A256835 (b=7), A256836 (b=8), A256837 (b=9), A256838 (b=10), A256839 (b=11), A256840 (b=12), A256841 (b=13).

Programs

Haskell

a256777 n = a256777_list !! (n-1)
a256777_list = [x | x <- map (+ 625) a000290_list, a010051' x == 1]

Mathematica

Select[Range[200]^2+625,PrimeQ] (* Harvey P. Dale, Aug 27 2025 *)

PARI

list(lim)=if(lim<641,return([])); my(v=List(),t); forstep(n=4, sqrtint(lim\1-625), 2, if(isprime(t=n^2+625), listput(v,t))); Vec(v) \\ Charles R Greathouse IV, Aug 18 2017