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

Author

Zak Seidov, May 10 2013

Keywords

• nonn
• easy

Comments

Or, primes p == {9, 14, 15, 22, 23, 28} (mod 37).

Corresponding values p^2 (mod 37): 11, 3, 7, 3, 11, 7, 7, 3, 11, 3, 3, 11, 7, 11, 11, 3, 7.

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