The a2b2 Conjecture - Vô Conjecture 5 Series 3 (VC5S3)

The a2b2 Conjecture (VC5S3) proposes that for every integer a>1, there exists an integer b such that: 0<b<e(lna)^2, a^2+b^2 is prime, b has the same parity as a+1; that is, if a is odd, b is even, and if a is even, b is odd. This Conjecture suggests that almost every integer a can generate a prime from the sum of two squares, with b being very small relative to a.