The ab2 Conjecture -Vô Conjecture 5 series 4 (VC5S4)

In this paper, we consider the ab2 conjecture, a proposal concerning the relationship between natural numbers and prime numbers through perfect squares. This conjecture states that for every natural number a>1, there exists a natural number b such that b<e(lna)^2 and a+b^2\in\mathbb{P}. We present preliminary observations, example tests, and a discussion of the difficulty of finding counterexamples.