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Association for Research on Math and Science
More Mersenne Primes


Ars Technica Team Prime Rib http://www.teamprimerib.com/
A distributed computing team dedicated to finding Mersenne prime numbers.
Distributed Computing Strikes Gold http://news.com.com/2100-1001-276972.html?legacy=cnet
An article about the newly found M_13466917 at CNET.com.
Internet PrimeNet Server http://www.mersenne.org/ips/
PrimeNet is a distributed computing project for the Great Internet Mersenne Prime Search, co-ordinating the assignment of work and collection of results.
Marin Mersenne http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Mersenne.html
Biography of the Minim friar and his contributions to number theory. Includes references, pictures, and cross-references to topics.
Mersenne and Fermat Primes Field http://ourworld.compuserve.com/homepages/hlifchitz/Henri/us/MersFermus.htm Henri Lifchitz's single general form contains the main remarkable numbers of number theory.



Mersenne Prime Digits http://www.isthe.com/chongo/tech/math/prime/mersenne.html
Landon Curt Noll lists the decimal, English, and American expansions of all the known Mersenne primes.
Mersenne Prime Mailing List http://www.ndatech.com/mersenne/signup.htm
Unmoderated list for communication between those interested in all aspects of Mersenne Primes. Sginup and access to archives.
Mersenne Prime Search http://www.mersenne.org/prime.htm
An organized search for Mersenne prime numbers. Free software provided.
Mersenne Primes: History, Theorems, and Lists http://www.utm.edu/research/primes/mersenne/
A comprehensive summary of Mersenne prime matters, from their earliest history to the modern test implementations by computer.
mersenneforum.org http://www.mersenneforum.org/
A forum about prime numbers and computerized searches for more of them. Includes discussions of software and hardware issues encountered by searchers.



The Mersenne Prime Homepage http://www.albanyconsort.com/mersenne/
Notes and links by Simon Rubinstein-Salzedo.
Will Edgington's Mersenne Page http://www.garlic.com/~wedgingt/mersenne.html
Downloadable factor data, newsletter archives, and proofs of theorems relating to the search for Mersenne primes.



Elliptic Curves and Modular Forms -Software


Aliquot http://archives.math.utk.edu/software/msdos/dynamics/aliquot/.html
A DOS tool to compute aliquot chains with small starting numbers, by Ivo Düntsch.
apfloat http://www.apfloat.org/
High-performance arbitrary precision arithmetic package for C++ and Java.
ARIBAS http://www.mathematik.uni-muenchen.de/~forster/sw/aribas.html
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.
CALC http://www.numbertheory.org/calc/krm_calc.html
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.
CLN - Class Library for Numbers http://www.ginac.de/CLN/
C++ library by Bruno Haible.




ECMNET
 http://www.loria.fr/~zimmerma/records/ecmnet.html
Elliptic curve factoring software.
Encyclopedia of Integer Sequences Seeker http://sourceforge.net/projects/eisseeker
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.
Factorizer http://www.hermetic.ch/factors/factors.htm
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 version online.
FTP Sites, Calculator Programs and Archives http://www.maths.uq.edu.au/~krm/N1.html
In the Number Theory Web.
Galois http://www.riaca.win.tue.nl/archive/can/SystemsOverview/Special/NumberTheory/Galois.html An algebra/number theory package by R. Lidl, R. W. Matthews and R. Wells.



giantint http://www.perfsci.com/free/giantint/index.html
Library of routines for large integer arithmetic and number theory.
GIMPS FAQ list http://www.mersenne.org/faq.htm
About the Mersenne Prime Freeware.
GNU MP Home Page http://www.swox.com/gmp/
Free library for arbitrary precision arithmetic.
GNUBC http://www.numbertheory.org/gnubc/gnubc.html
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.
HiPiLib - High Performance Libraries http://www.hipilib.de/
Home of PIOLOGIE, a library for arbitrary precision arithmetic, operating on natural, integer and rational numbers.



Implementations of Extended LLL http://www.math.uu.nl/people/vdkallen/lllimplementations.html
By Wilberd van der Kallen.
Java PHASER Project http://www.math.miami.edu/~phaser
An application for numerically and graphically analyzing dynamical systems.
Jim Howell Software http://home.netcom.com/~jrhowell/math/software.htm
Large integer arithmetic.
KANT / KASH http://www.math.tu-berlin.de/~kant/kash.html
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.
Kaprekar Series Generator http://kaprekar.sourceforge.net/
A java application for determining the Kaprekar Constants and Series for numbers in various radixes.



L http://pmmac03.math.uwaterloo.ca/~mrubinst/L_function_public/L.html
A C++ class library, datasets and command line program for computing zeros and values of L-functions, by Michael Rubinstein.
Large Number Arithmetic in BASIC http://www.home.zonnet.nl/vspickelen/Largefiles/LargeInt.htm
Library for large-integer arithmetic, plus some number theory modules.
LiDIA http://www.informatik.tu-darmstadt.de/TI/LiDIA/
C++ Library For Computational Number Theory.
Magma Computational Algebra System Home Page http://magma.maths.usyd.edu.au/
A large, well-supported software package for computationally hard problems in algebra, number theory, geometry and combinatorics.
MAGMA/PARI Calculator http://modular.fas.harvard.edu/calc/
Web interface for short programs in either language.



Maple Worksheets by John Cosgrave http://www.spd.dcu.ie/johnbcos/Maple.htm
A selection of Maple (V.5) worksheets for teaching purposes.
Math Archives Software http://archives.math.utk.edu/software/mac/numberTheory/.directory.html
Mac/Number Theory section.
Math Archives Software http://archives.math.utk.edu/software/msdos/number.theory
PC/Number Theory section.
Mersenne Prime Freeware http://www.samurai.com/mersenne/freeware.html
Freeware to search for Mersenne Primes. Pointers to FreeLIP, GMP, HFloat, apfloat, CALC.
MIRACL http://indigo.ie/~mscott/
Multiprecision Integer and Rational Arithmetic C/C++ Library.



Multiprecision Software Directory http://crd.lbl.gov/~dhbailey/mpdist/mpdist.html
Fortran multiprecision software by David H. Bailey of Lawrence Berkeley Lab.
NTL: A Library for doing Number Theory http://www.shoup.net/ntl/
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.
Number Field Sieve NET http://www.iaeste.dk/~henrik/projects/nfsnet.html
A client/server system for NFSNET by Henrik Olsen.
Number-Theoretic Hacks http://www.ics.uci.edu/~eppstein/numth/
Algorithms implemented by David Eppstein.
NZMATH http://tnt.math.metro-u.ac.jp/nzmath/
Python based number theory oriented calculation system, developed at Tokyo Metropolitan University. Downloads, mailing list.
Paul's TI-92 Number Theory Archive http://www.geocities.com/Hollywood/2979/ntheory.html
Download site for number theory programs adapted from UBASIC/MALM for the TI-92.
Schulenberg and Associates http://www.schulenberg.com/
Factoring programs. Windows, free download.
SIMATH http://tnt.math.metro-u.ac.jp/simath/
Computer algebra system for number theoretic applications.
ZEN http://fchabaud.free.fr/English/ZEN/
A toolbox for computation in finite rings, by Florent Chabaud and Reynald Lercier. ANSI-C source, free download, GPL.


Number Theory - Elliptic Curves - Modular Forms


APECS ftp://ftp.math.mcgill.ca/pub/apecs
FTP site for Ian McConnell's MAPLE programs.
Code to Compute Heights on Elliptic Curves http://www.institut.math.jussieu.fr/~girard/magma/anglais.html
Magma implementation of Silverman's algorithm to compute the canonical height on an elliptic curve over a number field or function field, by Martine Girard.
EIS http://www.mathi.uni-heidelberg.de/~bruinier/Readme.eis
Software for computing Fourier coefficients of Eisenstein series attached to lattices by M. Kuss and J. Bruinier. Binaries for x86-Linux.
Ellipsa http://www.ellipsa.net/
Includes Primo, an implementation of ECPP, and CPG, class polynomial builder.
Heegner Tools http://www.math.mcgill.ca/darmon/programs/heegner/heegner.html
Peter Green's Heegner Points package. Requires Linux and Pari/GP 2.1.1 or higher.



Modular Forms Software http://modular.fas.harvard.edu/Tables/software.html
HECKE can be used to compute basis of q-expansions and Hecke operators on fairly general spaces of modular forms.
Modular Quaternion Groups http://www.geocities.com/assafwool/Quat/Quat.html
Fundamental domains for Shimura curves, written in GAP. Documented with description of algorithms used and program structure, input and output. Results for quaternion algebras with discriminant up to 100.
Periods of Hilbert Modular Forms http://www.math.mcgill.ca/darmon/programs/logan/logan.html
A package of PARI programs (v.2.1.1 or higher) for calculations described in "Periods of Hilbert modular forms and rational points on elliptic curves" by H. Darmon and A. Logan.
TECC http://matha.e-one.uec.ac.jp/~kida/TECC.html
Tiny Elliptic Curve Calculator, by Masanari Kida. Requires KASH 2.2.




Number Theory


A Mechanical Proof of Quadratic Reciprocity http://www.onr.com/user/russ/david/gauss.html
A paper by David M. Russinoff describing the use of the Boyer-Moore theorem prover in mechanically generating a proof of the Law of Quadratic Reciprocity. PS/PDF.
About Two Months of Computing http://www.fourmilab.ch/documents/threeyears/two_months_more.html
Work on the 196 palindrome problem by Tim Irvin.
Application of Digital Root http://www.geocities.com/bappan420/
A test for the terms of a sequence being expressed by a polynomial, by Roupam Ghosh.
Covers, Sumsets and Zero-sums http://pweb.nju.edu.cn/zwsun/csz.htm
A unified approach to covering systems, restricted sumsets and zero-sum problems by Zhi-Wei Sun.
Fermat's Little Theorem http://www.pballew.net/FermLit.html
With notes on Carmichael numbers and the life of R.D. Carmichael.



Frequently Asked Questions http://db.uwaterloo.ca/~alopez-o/math-faq/node21.html
Number Theory section of the sci.math FAQ list.
Hakmem Continued Fractions http://www.inwap.com/pdp10/hbaker/hakmem/cf.html
Some notes from the MIT collection. Includes Gosper's algorithms for CF arithmetic.
Infinite Series Theorem http://www.infiniteseriestheorem.org/
Addresses the question whether a series of rational functions converges to a rational number.
Integer Relations http://www.cecm.sfu.ca/projects/IntegerRelations/
To determine linear integer dependence among numerical constants and to determine the minimal polynomial of an approximate algebraic number. Interactive or via email.
Introduction to Bernoulli Numbers http://numbers.computation.free.fr/Constants/Miscellaneous/bernoulli.html
A web article with a brief history and account of their relationship with the Riemann zeta function and Fermat's Last Theorem (HTML/PS).



Klein Polyhedra http://members.lycos.co.uk/keithmbriggs/klein-polyhedra.html
Examples and algorithms for computing Klein polyhedra, also known as Arnold sails or veils (voiles), by Keith Briggs.
L-Functions http://www.math.okstate.edu/~loriw/start/start.html
Classified by degree, then by level, then by eigenvalue, then by root number.
Lehmer's Conjecture http://www.cecm.sfu.ca/~mjm/Lehmer/lc.html
That the Mahler measure of an algebraic number is bounded away from 1. Pages by Michael Mossinghoff, UCLA.
Linear Independence Measures for Logarithms of Algebraic Numbers http://www.mathp6.jussieu.fr/~miw/articles/cetraro.html
Michel Waldschmidt. Cetraro summer school lectures, July 2000.
MathPages: Number Theory http://www.mathpages.com/home/inumber.htm
Kevin Brown's collection of sci.math postings related to number theory topics.



MathWorld Number Theory http://mathworld.wolfram.com/topics/NumberTheory.html
Index to articles in Eric Weisstein's MathWorld in the area of number theory.
Noncommutative Geometry, Trace Formulae and the Zeroes of the Riemann Zeta Function http://www.math.ohio-state.edu/lectures/connes/Connes_course.html
Lecture notes by Alain Connes.
Number Theory http://www.math.niu.edu/~rusin/known-math/index/11-XX.html
Dave Rusin's guide to number theory.
Number Theory http://www.alpertron.com.ar/NUMBERT.HTM
Proofs along with equation solvers and graphical views written in Java.
Number Theory Foundation http://www.math.uiuc.edu/ntf/
Aims to collect donations from supporters of number theory and to disburse these donations to encourage research.



Number Theory Glossary http://www.math.umbc.edu/~campbell/NumbThy/Class/Glossary.html
Compiled by Robert Campbell.
Number Theory Web http://www.numbertheory.org/ntw/
Things of interest to number theorists collected by Keith Matthews.
On-Line Encyclopedia of Integer Sequences http://www.research.att.com/~njas/sequences/
Given an integer sequence, find its name, and formula.
Online Seminar: Galois theory of p-Extensions http://public.csusm.edu/public/fhajir/kochbook.html
Email seminar on "Galoissche Theorie der p-Erweiterungen" by Helmut Koch.
Other Maths http://www.users.globalnet.co.uk/~perry/maths/othermaths.htm
A wide selection of number theory topics compiled by Jon Perry.



Some Highlights of Arithmetic Combinatorics http://www.math.ucla.edu/~tao/254a.1.03w/
Lecture notes and resources on combinatorial number theory by Terence Tao.
Some Number-Theoretical Constants http://www.gn-50uma.de/alula/essays/Moree/Moree.en.shtml
Products of rational functions of p over primes, computed by Gerhard Niklasch and Pieter Moree.
Somos Polynomials http://grail.cba.csuohio.edu/~somos/somospol.html
Related to Somos sequences and elliptic theta functions.
Square-free Gaps http://www.marmet.ca/louis/sqfgap/
Algorithm and source code for the calculation of square-free numbers and gaps.
The Arithmetic Properties of Binomial Coefficients http://www.cecm.sfu.ca/organics/papers/granville/index.html
Activated text by Andrew Granville.



The Canadian Number Theory Association http://members.rogers.com/superprof/cnta.html
A loosely defined group of individuals, mainly in Canada, active in research in Number Theory.
The Somos Sequence Site http://www.math.wisc.edu/~propp/somos.html
Web resources for information on Somos sequences and related topics such as elliptic divisibility sequences.
The Valuation Theory Home Page http://math.usask.ca/fvk/Valth.html
A forum for all mathematicians who work in valuation theory or apply valuation theoretical results in their own field of research.
The Work of Robert Langlands http://www.sunsite.ubc.ca/DigitalMathArchive/Langlands/intro.html
Thesis, papers, manuscripts, letters and bibliography.
Three Years of Computing http://www.fourmilab.ch/documents/threeyears/threeyears.html
Palindrome Quest. Reporting computations on the 196 problem.



Transcendental Numbers http://www.spd.dcu.ie/johnbcos/transcendental_numbers.htm
Maple worksheets, lecture notes and links to other resources by John Cosgrove.
Vignettes on Automorphic and Modular forms, Representations, L-functions, and Number Theory http://www.math.umn.edu/~garrett/m/v/
By Paul Garrett.
Visible Structures in Number Theory http://www.cecm.sfu.ca/~loki/Papers/Numbers/
By Peter Borwein and Loki Jörgenson. Recognising number patterns visually.
World Records for Numerical Palindromes http://www.jasondoucette.com/worldrecords.html
The 196 Palindrome Quest and The Most Delayed Palindromic Number, by Jason Doucette.



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