A346145 Primes of the form k^2 + 25.

29, 41, 61, 89, 281, 349, 509, 601, 701, 809, 1049, 1181, 1321, 1789, 2141, 2729, 3389, 4649, 5209, 5501, 5801, 8861, 9241, 9629, 10429, 11261, 11689, 12569, 15401, 15901, 17449, 17981, 18521, 19069, 21341, 21929, 23741, 24989, 26921, 27581, 33149, 39229, 40829, 41641, 42461, 45821, 46681, 52009

Offset: 1

Author

Todor Szimeonov, Jul 06 2021

Keywords

• nonn

Comments

k^2 + 25 = (k+5i)*(k-5i), where i is the imaginary unit.

Links

• Todor Szimeonov, A dramatic encounter

Crossrefs

Cf. A002144, A002496, A005473, A138353, A243451.

Programs

Mathematica

Select[Range[230]^2 + 25, PrimeQ] (* Amiram Eldar, Jul 06 2021 *)

PARI

list(lim)=my(v=List(),p); forstep(k=2,sqrtint(lim\1-25),2, if(isprime(p = k^2+25), listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Jul 06 2021

Formula

a(n) >> n log^2 n (Brun sieve). - Charles R Greathouse IV, Jul 06 2021