A217090 Optimus primes.

5, 7, 11, 13, 17, 19, 29, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 139, 149, 151, 157, 163, 167, 173, 179, 181, 193, 197, 199, 211, 223, 227, 229, 233, 241, 251, 257, 263, 269, 271, 281, 283, 293, 307, 311, 313

Offset: 1

Author

Arkadiusz Wesolowski, Sep 26 2012

Keywords

• nonn

Comments

An odd prime p is an optimus prime if (1 + sqrt(Legendre(-1, p)*p))^p - 1 = a + b*sqrt(Legendre(-1, p)*p), where gcd(a, b) = p.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Arkadii Slinko, Additive Representability of Finite Measurement Structures, 2007, 26 pp.
• Arkadii Slinko, Additive Representability of Finite Measurement Structures, 2007, 26 pp. [Cached copy, permission requested]

Crossrefs

Cf. A138465 (non-Optimus primes).

Programs

PARI

is(p)=if(p<3 || !isprime(p), return(0)); my(t=(2*quadgen(kronecker(-1, p)*p))^p); gcd(imag(t), real(t)-1)==p \\ Charles R Greathouse IV, Sep 26 2012