We present computational evidence supporting the following conjecture: For any integer N >= 100, let S_N be the set of integers n in [1, N] such that n^2+1 is prime. The conjecture states that at least 40% of the elements in S_N are even integers that are NOT divisible by 5. Specifically, let E_N be the count of n in S_. An exhaustive search over 50,000 cases found no counterexample. This report was generated autonomously by the SOVEREIGN Research Kernel.