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unexpected eof while reading","robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":false,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["gpgpu","gpu-computing","lucas-lehmer","mersenne-numbers","opencl"],"created_at":"2026-02-14T08:30:50.028Z","updated_at":"2026-02-14T08:30:51.164Z","avatar_url":"https://github.com/preda.png","language":"C","readme":"[![Actions Status](https://github.com/preda/gpuowl/actions/workflows/ci.yml/badge.svg?branch=master)](https://github.com/preda/gpuowl/actions/workflows/ci.yml)\n\n## Must read papers\n\n### Multiplication by FFT\n\n- [Discrete Weighted Transforms and Large Integer Arithmetic](https://www.ams.org/journals/mcom/1994-62-205/S0025-5718-1994-1185244-1/S0025-5718-1994-1185244-1.pdf), Richard Crandall and Barry Fagin, 1994\n- [Rapid Multiplication Modulo the Sum And Difference of Highly Composite Numbers](https://www.daemonology.net/papers/fft.pdf), Colin Percival, 2002\n\n### P-1\n\n- [An FFT Extension to the P-1 Factoring Algorithm](https://www.ams.org/journals/mcom/1990-54-190/S0025-5718-1990-1011444-3/S0025-5718-1990-1011444-3.pdf), Montgomerry \u0026 Silverman, 1990\n- [Improved Stage 2 to P+/-1 Factoring Algorithms](https://inria.hal.science/inria-00188192v3/document), Montgomerry \u0026 Kruppa, 2008\n\n\n# PRPLL\n\n## PRobable Prime and Lucas-Lehmer mersenne categorizer\n(pronounced *purrple categorizer*)\n\nPRPLL implements two primality tests for Mersenne numbers: PRP (\"PRobable Prime\") and LL (\"Lucas-Lehmer\") as the name suggests.\n\nPRPLL is an OpenCL (GPU) program for primality testing Mersenne numbers.\n\n\n## Build\n\nInvoke `make` in the source directory.\n\n\n## Use\nSee `prpll -h` for the command line options.\n\n\n## Why LL\n\nFor Mersenne primes search, the PRP test is by far preferred over LL, such that LL is not used anymore for search.\nBut LL is still used to verify a prime found by PRP (which is a very rare occurence).\n\n\n### Lucas-Lehmer (LL)\nThis is a test that proves whether a Mersenne number is prime or not, but without providing a factor in the case where it is not prime.\nThe Lucas-Lehmer test is very simple to describe: iterate the function f(x)=(x^2 - 2) modulo M(p) starting with the number 4. If\nafter p-2 iterations the result is 0, then M(p) is certainly prime, otherwise M(p) is certainly not prime.\n\nLucas-Lehmer, while a very efficient primality test, still takes a rather long time for large Mersenne numbers\n(on the order of weeks of intense compute), thus it is only applied to the Mersenne candidates that survived the cheaper preliminary\nfilters TF and P-1.\n\n### PRP\nThe probable prime test can prove that a candidate is composite (without providing a factor), but does not prove that a candidate\nis prime (only stating that it _probably_ is prime) -- although in practice the difference between probable prime and proved\nprime is extremely small for large Mersenne candidates.\n\nThe PRP test is very similar computationally to LL: PRP iterates f(x) = x^2 modulo M(p) starting from 3. If after p iterations the result is 9 modulo M(p), then M(p) is probably prime, otherwise M(p) is certainly not prime. The cost\nof PRP is exactly the same as LL.\n","funding_links":[],"categories":[],"sub_categories":[],"project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fpreda%2Fgpuowl","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fpreda%2Fgpuowl","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fpreda%2Fgpuowl/lists"}