%I #23 May 22 2017 11:54:45

%S 5,7,11,13,17,19,29,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,

%T 107,109,113,127,131,139,149,151,157,163,167,173,179,181,193,197,199,

%U 211,223,227,229,233,241,251,257,263,269,271,281,283,293,307,311,313

%N Optimus primes.

%C 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.

%H Charles R Greathouse IV, <a href="/A217090/b217090.txt">Table of n, a(n) for n = 1..10000</a>

%H Arkadii Slinko, <a href="http://www.math.auckland.ac.nz/~slinko/Research/survey5.pdf">Additive Representability of Finite Measurement Structures</a>, 2007, 26 pp.

%H Arkadii Slinko, <a href="/A217090/a217090.pdf">Additive Representability of Finite Measurement Structures</a>, 2007, 26 pp. [Cached copy, permission requested]

%o (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

%Y Cf. A138465 (non-Optimus primes).

%K nonn

%O 1,1

%A _Arkadiusz Wesolowski_, Sep 26 2012