We present Project Goliath, a high-performance computational framework for exhaustively searching for counterexamples to the Beal Conjecture. Utilizing a novel 20-prime localized residue sieve implemented in C/AVX2, we have established a new industrial benchmark by verifying over 2.25 Trillion candidate pairs. This research clearing the "Miracle Zone" up to 1,000,000 bases significantly strengthens the heuristic evidence for the conjecture's validity.
Rynaldo Stoltz Rynaldo Stoltz (Thu,) studied this question.