New Computational Bounds for the Beal Conjecture via Localized Residue Sieving

Zenodo (CERN European Organization for Nuclear Research) 2026 Preprint Open access

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Authors: Stoltz Rynaldo
DOI: 10.5281/zenodo.18491335
Cited by: 0

Abstract

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.

Fields of Study & Subjects

Analytic Number Theory Research Algebraic Geometry and Number Theory Cryptography and Residue Arithmetic

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
5 February 2026
Language
EN
Document type
Preprint