SRBase is a volunteer computing project dedicated to proving variants of the Sierpiński and Riesel conjectures — classical open problems in number theory — for every integer base from 2 to 1030. PrimeGrid works on the original (base-2) version of these problems; SRBase generalizes the search to every base that hasn't already been resolved elsewhere.
The Sierpiński problem asks: for a fixed base b, what is the smallest odd positive integer k such that k·bⁿ+1 is composite for every n ≥ 1? The Riesel problem asks the analogous question for k·bⁿ-1. Known and conjectured answers exist, but proving them requires systematically eliminating every smaller candidate by finding at least one prime value of k·bⁿ±1. For many bases, only a handful of candidate k values remain — each demanding primality tests on astronomically large n.
The project operates in collaboration with the Mersenne CRUS (Conjectures R Us) effort and uses specialized primality-testing software (LLR2 and PRST) heavily optimized for modern CPUs with AVX-512. Recent updates added multi-GPU sieving support and compatibility with Intel Arc graphics (early 2026), significantly accelerating candidate elimination.
SRBase holds several world-record prime discoveries for specific k·bⁿ forms and has substantially narrowed the open cases in the generalized Sierpiński-Riesel landscape. For PrimeGrid volunteers seeking a fresh challenge in prime number theory, SRBase is the natural next step.