Software

ECPP
An Elliptic Curve Primality Proving program by François Morain. Author has later implemented fastECPP which is not publicly available.
http://www.lix.polytechnique.fr/~morain/Prgms/ecpp.english.html

Glucas - Yet Another FFT
Free software program to test primality of Mersenne numbers (numbers with the form 2^n - 1).
http://www.oxixares.com/glucas/

Jean Penné's LLR
Proves k*2^n-1 with the Lucas-Lehmer-Riesel algorithm and k*2^n+1 with Proth's theorem. Free Windows and Linux download.
http://primes.utm.edu/bios/page.php?id=431

Paul Jobling's NewPGen
Sieving program for various listed forms involving a power or primorial. Page has introduction and free downloads for Windows or Linux.
http://primes.utm.edu/programs/NewPGen/

Prime Number Spiral
Windows software for exploring the Prime Number (Ulam's) Spiral. Online purchase.
http://www.hermetic.ch/pns/pns.htm

Primo
Elliptic Curve Primality Proving program which has set monoprocessor ECPP records. Windows freeware by Marcel Martin.
http://www.ellipsa.net/

Yahoo Groups: Primeform
Discussion group for PrimeFormGW and prime numbers. Program can trial factor and probable prime test any number, and prove many forms. Free Windows and Linux downloads after joining group.
http://groups.yahoo.com/group/primeform/

Yves Gallot's Proth.exe
Program to prove large primes on the form k*2^n+/-1. Page has introduction and free Windows download.
http://primes.utm.edu/programs/gallot/