A225550 Primes p such that p^2 mod 37 is prime.
23, 59, 83, 89, 97, 139, 157, 163, 199, 281, 311, 347, 379, 421, 467, 503, 509, 541, 569, 577, 601, 607, 643, 823, 829, 911, 947, 953, 971, 977, 1013, 1021, 1051, 1087, 1193, 1249, 1429, 1471, 1489, 1531, 1613, 1619, 1637, 1693, 1753, 1873, 1901, 1933, 2063, 2081, 2087, 2131, 2137, 2161, 2243, 2309, 2377, 2383, 2531
Offset: 1
Examples
23^2 = 529 and 529 mod 37 = 11 (prime).
Crossrefs
Cf. A045432.
Programs
-
Magma
[p: p in PrimesUpTo(3000) | IsPrime(p^2 mod 37)]; // Bruno Berselli, May 10 2013
-
Mathematica
Select[Prime[Range[2400]], PrimeQ[PowerMod[#, 2, 37]] &]
-
PARI
forprime (p = 2, 2351, isprime (p^2 %37) & print1 (p ", "))
Formula
a(n) ~ 6n log n. - Charles R Greathouse IV, May 10 2013
Comments