LiDIA
- C++ Library For Computational Number Theory.
- http://www.cdc.informatik.tu-darmstadt.de/TI/LiDIA/

cBigNumber
- Portable C++ class for integers with unlimited range, designed to be fast, functional and simple in use.
- http://www.imach.uran.ru/cbignum/

Large Number Arithmetic in BASIC
- Library for large-integer arithmetic, plus some number theory modules.
- http://largeint.sourceforge.net/

SAGE
- System for Arithmetic Geometry Experimentation: a framework for number theory, algebra, and geometry, initially designed for computing with elliptic curves and modular forms, by William Stein. Open source under GPL.
- http://modular.fas.harvard.edu/SAGE/

p-adic Arithmetic
- A Mathematica package by Stany De Smedt.
- http://library.wolfram.com/infocenter/MathSource/556/

Multiprecision Software Directory
- Fortran multiprecision software by David H. Bailey of Lawrence Berkeley Lab.
- http://crd.lbl.gov/~dhbailey/mpdist/mpdist.html

Kaprekar Series Generator
- A java application for determining the Kaprekar Constants and Series for numbers in various radixes.
- http://kaprekar.sourceforge.net/

L
- A C++ class library, datasets and command line program for computing zeros and values of L-functions, by Michael Rubinstein.
- http://pmmac03.math.uwaterloo.ca/~mrubinst/L_function_public/L.html

Encyclopedia of Integer Sequences Seeker
- EIS-Seeker is a libguile-based scheme interpreter devoted to the study of the Encyclopedia of Integer Sequences database. It is intended to help find new relations between sequences. C/Scheme, Posix.
- http://sourceforge.net/projects/eisseeker

NZMATH
- Python based number theory oriented calculation system, developed at Tokyo Metropolitan University. Downloads, mailing list.
- http://tnt.math.metro-u.ac.jp/nzmath/

Magma Computational Algebra System Home Page
- A large, well-supported software package for computationally hard problems in algebra, number theory, geometry and combinatorics.
- http://magma.maths.usyd.edu.au/

MAGMA/PARI Calculator
- Web interface for short programs in either language.
- http://modular.fas.harvard.edu/calc/

Factorizer
- A Windows program to find all factors of any positive integer less than 2^31 - 1; decompose numbers into their prime constituents; find prime numbersand pairs of primes; and to plot Erdos-Kac and Palmen Color histograms. Down load free demo, order full v
- http://www.hermetic.ch/factors/factors.htm

GNUBC
- Supports arbitrary precision integer arithmetic calculations with interactive execution: it is a superior version of the basic bc program which comes with the UNIX operating system. Keith Matthews has written several number-theoretic programs.
- http://www.numbertheory.org/gnubc/gnubc.html

CALC
- A calculator program for doing arbitrary precision integer arithmetic, written in ANSI C and Yacc, with a number of built-in functions for number theory, by Keith Matthews.
- http://www.numbertheory.org/calc/krm_calc.html

Galois
- An algebra/number theory package by R. Lidl, R. W. Matthews and R. Wells.
- http://www.riaca.win.tue.nl/archive/can/SystemsOverview/Special/NumberTheory/Galois.html

SIMATH
- Computer algebra system for number theoretic applications.
- http://tnt.math.metro-u.ac.jp/simath/

apfloat
- High-performance arbitrary precision arithmetic package for C++ and Java.
- http://www.apfloat.org/

Java PHASER Project
- An application for numerically and graphically analyzing dynamical systems.
- http://www.math.miami.edu/~phaser

Aliquot
- A DOS tool to compute aliquot chains with small starting numbers, by Ivo Düntsch.
- http://archives.math.utk.edu/software/msdos/dynamics/aliquot/.html

Number Field Sieve NET
- A client/server system for NFSNET by Henrik Olsen.
- http://www.iaeste.dk/~henrik/projects/nfsnet.html

Number-Theoretic Hacks
- Algorithms implemented by David Eppstein.
- http://www.ics.uci.edu/~eppstein/numth/

CLN - Class Library for Numbers
- C++ library by Bruno Haible.
- http://www.ginac.de/CLN/

Schulenberg and Associates
- Factoring programs. Windows, free download.
- http://www.schulenberg.com/

HiPiLib - High Performance Libraries
- Home of PIOLOGIE, a library for arbitrary precision arithmetic, operating on natural, integer and rational numbers.
- http://www.hipilib.de/

ECMNET
- Elliptic curve factoring software.
- http://www.loria.fr/~zimmerma/records/ecmnet.html

GIMPS FAQ list
- About the Mersenne Prime Freeware.
- http://www.mersenne.org/faq.htm

FTP Sites, Calculator Programs and Archives
- In the Number Theory Web.
- http://www.maths.uq.edu.au/~krm/N1.html

Math Archives Software
- Mac/Number Theory section.
- http://archives.math.utk.edu/software/mac/numberTheory/.directory.html

GNU MP Home Page
- Free library for arbitrary precision arithmetic.
- http://www.swox.com/gmp/

MIRACL
- Multiprecision Integer and Rational Arithmetic C/C++ Library.
- http://indigo.ie/~mscott/

giantint
- Library of routines for large integer arithmetic and number theory.
- http://www.perfsci.com/free/giantint/index.html

Implementations of Extended LLL
- By Wilberd van der Kallen.
- http://www.math.uu.nl/people/vdkallen/lllimplementations.html

NTL: A Library for doing Number Theory
- A high-performance, portable C++ library providing data structures and algorithms for manipulating signed, arbitrary length integers, and for vectors, matrices, and polynomials over the integers and over finite fields.
- http://www.shoup.net/ntl/

Maple Worksheets by John Cosgrave
- A selection of Maple (V.5) worksheets for teaching purposes.
- http://www.spd.dcu.ie/johnbcos/Maple.htm

ARIBAS
- An interactive interpreter for big integer and multi-precision floating point arithmetic with a Pascal/Modula like syntax. It has several builtin functions for algorithmic number theory.
- http://www.mathematik.uni-muenchen.de/~forster/sw/aribas.html

KANT / KASH
- KANT is a software package for sophisticated computations in number fields and in global function fields. With KASH you are able to use the powerful KANT V4 functions within a shell.
- http://www.math.tu-berlin.de/~kant/kash.html