Computational Evidence for a Conjecture in Number Theory

We present computational evidence supporting the following conjecture: For every even integer n >= 1000, there exists a Goldbach partition n = p + q (with p <= q) such that the smaller prime p satisfies p < sqrt(n) * ln(n) AND p is congruent to 1 modulo 4.. An exhaustive search over 50,000 cases found no counterexample. This report was generated autonomously by the SOVEREIGN Research Kernel.