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putil : primality testing, search and factorization utility

putil is a small tool for testing primality and finding the prime decomposition of a given integer as well as searching for primes of any given bit-length.

It has 4 major modes:

  • fac find prime factorizations
  • mrt probabilistic test for primality using ⌈log₄(n)⌉ rounds of the Miller-Rabin algorithm
  • llt deterministic primality test for Mersenne numbers using the Lucas-Lehmer algorithm
  • fpp pseudo-random search for probable primes of a given bit-length using Miller-Rabin

These 4 modes accept positive integers only.

Mersenne primes are prime numbers of the form 2ᵖ-1. In Lucas-Lehmer test mode it assumes you are passing only the Mersenne exponent p. Do not pass the actual value of the Mersenne number or you will be waiting for eons.

In prime search mode, locating large primes can take a long time on desktop computers depending on the bit-length you query. Anything larger than 8192 bits will require a coffee break.

Compiling

First, refresh the cabal package list.

      cabal update

The cmdargs, sscript and integer-logarithms libraries are required.

      cabal install cmdargs sscript integer-logarithms

Compile with -O2 and multi-core optimizations:

      ghc -o putil -O2 -threaded Main.hs

Running

If you compiled with multi-core support, run the putil utility with +RTS -N appended to the command and the Haskell runtime will automatically detect the number of cores your system has and use them when possible.

Examples

> putil fac 3895462145894328
2^3 x 3^3 x 18034546971733

> putil mrt 18848997157
Composite

> putil llt 110503
Prime

> putil fpp 64 3
[15223910619379001233,17858347140586802539,12182162899075669723]

Help message

putil v1.0, (A) github.com/fuvvy
Primality testing and prime factorization utility

putil [COMMAND] ... [OPTIONS]
  Examples:
   putil fac 3895462145894328
   putil mrt 18848997157
   putil llt 110503
   putil fpp 1024 3

Common flags:
  -? --help             Display help message
  -V --version          Print version information
     --numeric-version  Print just the version number

putil fac [OPTIONS] COMPOSITE-INTEGER
  Find prime factors

putil mrt [OPTIONS] TEST-INTEGER
  Test for primality using ⌈log₄(n)⌉ rounds of Miller-Rabin

putil llt [OPTIONS] MERSENNE-EXPONENT
  Test mersenne number for primality using Lucas-Lehmer

putil fpp [OPTIONS] BIT-LENGTH NUM-PRIMES
  Pseudo-random search for NUM-PRIMES probable primes of size BIT-LENGTH using
  Miller-Rabin