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Primes p such that p^2 mod 37 is prime.
1

%I #15 Sep 08 2022 08:46:05

%S 23,59,83,89,97,139,157,163,199,281,311,347,379,421,467,503,509,541,

%T 569,577,601,607,643,823,829,911,947,953,971,977,1013,1021,1051,1087,

%U 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

%N Primes p such that p^2 mod 37 is prime.

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

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

%F a(n) ~ 6n log n. - _Charles R Greathouse IV_, May 10 2013

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

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

%o (PARI) forprime (p = 2, 2351, isprime (p^2 %37) & print1 (p ", "))

%o (Magma) [p: p in PrimesUpTo(3000) | IsPrime(p^2 mod 37)]; // _Bruno Berselli_, May 10 2013

%Y Cf. A045432.

%K nonn,easy

%O 1,1

%A _Zak Seidov_, May 10 2013