A266954 Primes of the form p = a^2 + b^2 where neither |a+b| nor |a-b| is prime.

41, 113, 313, 353, 613, 653, 677, 761, 857, 977, 1013, 1201, 1301, 1373, 1553, 1613, 1733, 1877, 1913, 2113, 2153, 2213, 2237, 2273, 2297, 2333, 2381, 2477, 2657, 2693, 2713, 3137, 3313, 3329, 3413, 3581, 3593, 3613, 3833, 4013, 4157, 4253, 4373, 4397, 4481

Offset: 1

Author

Robert Israel, Jan 06 2016

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Mathematics Stack Exchange, A curious pattern on primes congruent to 1 mod 4

Programs

Maple

filter:= proc(q) local t,p;
      if not isprime(q) then return false fi;
      t:= op(op(1,GaussInt:-GIfactor(q)));
    p:= [abs(Re(t)+Im(t)),abs(Re(t)-Im(t))];
    not isprime(p[1]) and not isprime(p[2])
end proc:
select(filter, [seq(i, i=1..10000, 4)]);

Mathematica

lst = {}; Do[If[PrimeQ[a^2 + b^2] && ! PrimeQ[a + b] && ! PrimeQ[a - b], AppendTo[lst, a^2 + b^2]], {a, 2, 67}, {b, a -1}]; Take[ Union@ lst, 50] (* Robert G. Wilson v, Jan 06 2016 *)