Top Software Collection for Prime Numbers

PRP / Primality Testing Software
Software Source uses CPU / MT uses GPU OS support Developer Description Discussion thread(s)
Prime95 v30.19 / mprime Win32/64, Linux, MacOS George Woltman Mersenne Prime Search Software incl. multiple factoring methods
  (P-1, P+1, ECM) for Mersennes & similar forms
gpuowl / prpll v0.15
OpenCL
Win64, MacOS Preda Mihăilescu GPU Mersenne primality test
CUDALucas v2.06
CUDA
Win32/64, Linux Shoichiro Yamada Lucas-Lehmer primality test for Mersenne numbers
MLucas v21 Win32/64, Linux, MacOS Ernst Mayer Lucas-Lehmer primality test for Mersenne numbers
  incl. PRP & P-1 factoring for Mersennes; Pepin test & P-1 for Fermat numbers
Primo for Linux v4.3.3 Linux Marcel Martin Primality proving software via ECPP
Primo for Windows v3.0.9 Win32/64 Marcel Martin Primality proving software via ECPP incl. licence to provide
CM v0.4.4 Win32/64, Linux Andreas Enge Primality proving software via ECPP
PARI/GP v2.17.2 Win32/64, MacOS the PARI group math software incl. primality proving
PRST v13.1 Win32/64, Linux, MacOS Pavel Atnashev PRP and primality test
OpenPFGW v4.1.4 Win32/64, Linux Mark Rodenkirch PRP and primality test
LLR v4.0.7 / llrCUDA v4.0.0
CUDA
Win32/64, Linux, MacOS
  Console Application
Jean Penné PRP and primality test
LLR2 v1.3.3 Win32/64, Linux, MacOS Pavel Atnashev PRP and primality test for k • bn + c , bn - bm + c
proth20
OpenCL
Win32/64, Linux Yves Gallot Fast primality test for Proth numbers
genefer22
OpenCL
Win64, Linux, MacOS Yves Gallot Fast primality test for Generalized Fermat Numbers
VFYPR 16-bit DOS Tony Forbes Primality test for numbers
CH-G David Broadhurst CH-G primality proofs via PARI/GP - script


Client/Server applications used for sieving, factoring, and primality testing
Software Source uses CPU / MT uses GPU OS support Developer Description Discussion thread(s)
PRPNet v5.9.0 Mark Rodenkirch PRPNet is a distributed Client/Server application that can used to manage
  and perform probable prime (PRP) tests on a list of candidate numbers.
BOINC v8.x Win32/64, Linux, MacOS University of California Provide your unused computing power available for science.
AutoPrimeNet v1.0.2 Win, Linux, MacOS Teal Dulcet Automated assignment handler program for third party GIMPS software,
  including Mlucas, GpuOwl, PRPLL, CUDALucas, mfaktc and mfakto.
ECMNET Network to factorise numbers via ECM. Now powered by BOINC


Sieving Software
Software Source uses CPU / MT uses GPU OS support Developer Description Discussion thread(s)
mtsieve v.2.6.3
    • afsieve / afsievecl
    • ccsieve
    • cksieve / cksievecl
    • gcwsieve / gcwsievecl
    • dmdsieve
    • fbncsieve
    • fkbnsieve
    • gfndsieve / gfndsievecl
    • k1b2sieve
    • kbbsieve
    • lifsieve /lifsievecl
    • mfsieve / mfsievecl
    • pixsieve / pixsievecl
    • psieve / psievecl
    • sgsieve
    • smsieve / smsievecl
    • srsieve2 / srsieve2cl
    • twinsieve
    • xyyxsieve / xyyxsievecl
    • hcwsieve / hcwsievecl

OpenCL
Win64, Linux, MacOS Mark Rodenkirch
    • afsieve: find factors of alternating factorials
    • ccsieve: sieve for Cunningham Chains
    • cksieve: find factors of generalized Carol / Kynea numbers; (bn ± 1)2 - 2
    • gcwsieve: find factors of generalized Cullen / Woodall numbers; n • bn ± 1
    • dmdsieve: find factors of 2(2p - 1) - 1
    • fbncsieve: find factors of k • bn + c with b,n,c are fixed
    • fkbnsieve: find factors of k • bn + c with k,b,n are fixed
    • gfndsieve: find factors of k • 2n + 1 with k,n are variable
    • k1b2sieve: find factors of k • 2n + c with n,c are variable
    • kbbsieve: find factors of k • bb ± 1
    • lifsieve: find factors of xx ± yy ( Lifchitz numbers )
    • mfsieve: find factors of multi-factorials
    • pixsieve: find factors of substrings of a decimal string
    • psieve: find factors of primorials
    • sgsieve: for Sophie-Germain prime searches for k • bn - 1 with b,n are fixed
    • smsieve: find factors of Smarandache numbers
    • srsieve2: find factors of k • bn + c with b is fixed
    • twinsieve: find factors of k • bn ± 1 with b,n are fixed
    • xyyxsieve: find factors of xy ± yx ( Leyland numbers )
    • hcwsieve: find factors of bn • nb ± 1 ( generalized Hyper-Woodall / Cullen )

srbsieve v1.9 Win32/64 Gary Barnes Sieve for Sierpinski/Riesel primes to given base b
srbsieve_mthd Win32/64 Gary Barnes Sieve for Sierpinski/Riesel primes to given base b
NewPGen v2.82 Win32/64, Linux,
  Console Application
Paul Jobling Sieving software for different types of prime numbers
  Support primorial mode.
GFNSvCUDA v.07
CUDA
Win32 Anand Nair Sieve for Generalized Fermat Numbers (GFN)
tpsieve v0.2.3
CUDA
Win32/64, Linux, MacOS Geoff Reynolds Sieving software for twin primes
gfnsieve_ocl
OpenCL
Linux, MacOS Roman Trunov Sieve for Generalized Fermat Numbers (GFN)
PCWsieve v23.4.30
OpenCL
Win64, Linux64 B. Little, K. Brazier,
  Geoff Reynolds
Sieving software for Proth/Riesel/Cullen/Woodall primes
ppsieve v0.2.3
CUDA
Win32/64, Linux Ken Brazier Sieving software for Proth/Riesel primes
srsieve v1.1.4 Win64, Linux, MacOS Geoff Reynolds Specialised for a single sequence k • bn + c
sr1sieve v1.4.6 Win64 Linux, MacOS Geoff Reynolds Specialised for a single sequence k • bn ± 1
sr2sieve v2.0.0 Win64, Linux, MacOS Geoff Reynolds Specialised for a sequence k • bn ± 1 & bn ± k
fsievecl64 v1.0
OpenCL
Win64 Mark Rodenkirch Sieving software for n! ± 1
fnsievecl64 v1.0
OpenCL
Win64 Mark Rodenkirch Sieving software for k • bn + c where k,b,n are fixed
APSieve v0.68 Win32/64 Michael Bell, Jim Fougeron Sieving software for tuples of primes
  Support primorial mode
primesieve v12.8 Win32/64, Linux, MacOS Kim Walisch Prime ( k-tuplet ) counting software
primecount v7.19 Win64 Kim Walisch Calculating number of primes to a specific limit
Proth v7.2 Win32/64 Yves Gallot Sieving software for proth primes
TwinGen v2.2.5 Win32/64 David Underbakke Sieving software for twins
AthGFN64 Win32/64 David Underbakke,
  Yves Gallot, Phil Carmody
Sieving software
prime-gaps-cuda
CUDA
Linux, WSL Brian Kehrig A highly optimized GPU-accelerated program for finding large prime gaps.
EMSieve Win32/64, Linux Serge Batalov A sieve/prefactor program for the Eisenstein-Mersenne Primes:
  3p ± 3(p + 1)/2 + 1


Factoring Software
Software Source uses CPU / MT uses GPU OS support Developer Description Discussion thread(s)
YAFU v3.0 Win32/64, Linux, MacOS Ben Buhrow Factoring software
GMP-ECM v7.0.5
CUDA
Win32/64, Linux, MacOS Open source implementation Factoring software
CUDAPm1 v0.22
CUDA
Win32/64, Linux ? P-1 Factoring software for Mersenne numbers,
  based on CUDALucas
cudaWagstaff v0.03
CUDA
Win32/64 ? Factoring Software for Wagstaff numbers
GGNFS v0.77 Win32/64 ? A Number Field Sieve implementation
Mfactor Win64 Ernst Mayer Factoring Software for Mersenne numbers
gfsieve v24.9
OpenCL
Win64, Linux Yves Gallot Factoring Software for Fermat numbers
mmff v0.28
CUDA
Win64 George Woltman Factoring Software for double Mersenne numbers
  and small Fermat numbers
MSieve v15.3
CUDA
Win32/64 ? Factoring Software for large integers
mfaktc v0.24
CUDA
Win32/64, Linux ? Factoring Software for GIMPS - Mersenne numbers
mfakto v0.16
OpenCL
Win64 Bertram Franz Factoring Software for GIMPS - Mersenne numbers
mfaktp v0.02.1
CUDA
Win64 ? Factoring Software for GIMPS - Mersenne numbers
gvtf
Vulkan
Win64 ? Trial factoring implementation for mersenne primes
CADO-NFS Linux, MacOS, Win64 Number Field Sieve algorithm for factoring integers
aliqueit v1.13 Win32/64, Linux Mikael Klasson, Christian Beer Computing and verifying aliquot sequences