PrimeGrid

PrimeGrid is a volunteer computing project dedicated to finding large prime numbers and solving long-standing open problems in number theory — one of the oldest and most fundamental branches of mathematics. The project runs multiple concurrent sub-projects, each targeting a different class of primes: Generalized Fermat primes, Sierpiński and Riesel number problems, Woodall primes, Cullen primes, Proth primes, and more.

Prime numbers — integers greater than 1 that are divisible only by 1 and themselves — have fascinated mathematicians for over two thousand years. Despite their apparent simplicity, primes exhibit deep and often mysterious patterns that remain at the heart of active mathematical research. Some of the problems PrimeGrid works on are directly related to famous unsolved conjectures. For example, the Sierpiński problem (first posed in 1960) asks whether a specific number is the smallest Sierpiński number; PrimeGrid systematically eliminates candidates by finding prime values of the form k × 2ⁿ + 1.

PrimeGrid's computational toolkit revolves around two primality engines. LLR (Lucas-Lehmer-Riesel) runs deterministic primality tests on numbers of the form k·bⁿ±1 — the workhorse for the Sierpiński, Riesel, Proth, Cullen, and Woodall searches. Genefer runs Fermat probable-prime tests on Generalized Fermat candidates of the form b²ⁿ+1, with verified follow-up once a PRP is found. Separate sieving passes pre-filter obvious composites before those expensive tests run. All apps are heavily optimized for modern CPU vector instructions (AVX-512, FMA) and for GPUs where supported, and can test numbers with millions of digits. Note that Mersenne primes (2^p-1) are the territory of GIMPS, not PrimeGrid.

PrimeGrid has discovered numerous world-record primes, including some of the largest known non-Mersenne primes. Beyond pure mathematics, prime number research has deep connections to cryptography — the RSA encryption algorithm that secures internet commerce depends fundamentally on the difficulty of factoring large numbers into their prime components. The project also maintains an active community with competitive challenges and recognition for volunteers who make discoveries.