Accelerating the Search for Mersenne Primes: A Front-End Pre-Screening Pipeline for GIMPS — Stanford

Abstract We present a front-end pipeline for GIMPS that pre-screens Mersenne prime candidates before they enter the GIMPS workflow. The pipeline uses a proven Prime Generator (deterministic Miller-Rabin up to 3.215×10^9) and a new Small Divisor Test (H2) that eliminates candidates with small prime factors using precomputed multiplicative orders. Surviving candidates are ranked by empirically derived priority heuristics (S1, S4, S6, S7). The pipeline reduces the number of candidates entering GIMPS by approximately 85%, lowers pre-screening costs, and prioritizes the most promising candidates first. All hard filters are mathematically proven; all heuristics are clearly labeled as empirical. Validated on all 52 known Mersenne primes and on all historical gaps from MP#1 to MP#30, the pipeline consistently identified the next Mersenne prime and ranked it Green (highest priority). The pipeline does not replace GIMPS — it makes GIMPS faster and more efficient.