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

1,1

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.

Links

Table of n, a(n) for n=1..59.

Formula

a(n) ~ 6n log n. - Charles R Greathouse IV, May 10 2013

Example

23^2 = 529 and 529 mod 37 = 11 (prime).

Mathematica

Select[Prime[Range[2400]], PrimeQ[PowerMod[#, 2, 37]] &]

Prog

(PARI) forprime (p = 2, 2351, isprime (p^2 %37) & print1 (p ", "))
(Magma) [p: p in PrimesUpTo(3000) | IsPrime(p^2 mod 37)]; // Bruno Berselli, May 10 2013

Crossrefs

Cf. A045432.

Sequence in context: A043169 A043949 A005111 * A179629 A274381 A044125

Adjacent sequences: A225547 A225548 A225549 * A225551 A225552 A225553

Keyword

nonn,easy

Author

Zak Seidov, May 10 2013

Status

approved