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Carmichael Numbers and the Miller-Rabin Test - A worksheet from Professor Alexandre Borovik containing practical examples where Fermat probable primality fails to identify composites, yet strong probable primality can resolve.

Deficient Factorials - A summary of all known searches for primes of the form n!/k+-1 (with k>1), n!/k!+-1 (k>3) and n!/n#+-1.

Generalized Woodall Numbers - An organized search for primes of the form n*b^n-1.

Henri Lifchitz - Research in number theory, prime numbers and parity of arithmetic functions. Includes primality testing theorems and prime number chains. In English and French.

Least Primitive Root of Prime Numbers - Empirical and statistical results showing the smallest base required to prove a number is prime. Includes theory and conjectures.

Lucas Sequences in Cryptography - Focus on their use in primality testing, with pseudo-code. Includes an explanation of the strong Lucas PRP test.

Lucas's Primality Test With Factored N-1 - Kevin Brown explains the mathematics behind the classical "N-1" primality testing algorithm.

Multifactorial Primes - An organized search for primes of the form n!!!...!!!! +/-1. Includes table of numbers searched and primes found.

Perrin Numbers - Includes details of primality testing using the Perrin sequence, listing the first 17 Perrin pseudoprimes.

Primality Proving - Finding Primes and Proving Primality; Quick Tests for Small Numbers and Probable Primes. Yves Gallot's Proth.exe program for Windows is also available from these pages.

Primality Testing - The problem of primality testing and factorization are two distinct problems. If we concentrate on primality testing, we never need to know the actual factors. The only question to be answered is "is the number in question prime or composite."

Primality Testing Applet - A small Java applet to interactively perform strong probable primality tests.

Pseudoprimes/Probable Primes - Jon Grantham's papers on pseudoprimality tests and their generalizations, including Frobenius pseudoprimality and the as-yet unanswered '$620 question'.

Richard Pinch - Mathematics Research - A list of Richard Pinch's publications, including his lists of Carmichael numbers and pseudoprimes.

Search for Prime Numbers - Search of the next prime of the form n!+1. Project information, software download, and results.

Systematic Search of Primes of the Form k*2^n+1 - Nestor Sérgio de Araújo Melo extends the searches for Proth primes, Keller primes and Fermat factors to higher limits.

Yahoo Groups : PrimeForm - Discussion group for the primality-testing program, PrimeForm. Includes links to the PrimeForm program's home page, contact and download information.

Yves Gallot's Proth Search Page - A list of prime number searches using Yves Gallot's proth.exe program, available to download. Maintained by Ray Ballinger.

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