Ask Dr. Math What is a prime number? How can you find prime numbers? What's the 'Sieve of Eratosthenes'? What's the largest known prime?
Basic Theorems Concerning Prime Numbers An introductory page on the theory of prime numbers with proofs of some important theorems including the infinitude of primes, Euclid's algorithm and the fundamental theorem of arithmetic.
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.
Distribution of the Prime Numbers Web article by Johan G. van der Galiën showing that the primes do not satisfy certain statistical tests for randomness.
EFF Cooperative Computing Awards Between $100,000 and $250,000 will go to the first individual or group who discovers a new prime number above 10 million digits.
Electronic Frontier Foundation Cash prizes for discovery of very large prime numbers through Cooperative Computing Awards program.
Elliptic Curve Primality Proving Algorithm The ECPP is a modern method of primality proving that does not require auxiliary factorizations. Instead, ECPP uses the sizes of groups of rational points on elliptic curves modulo n.
Formulae for Determining Primality or Compositeness This is a method to produce formulas of various complexities with real coeffecients whose itereation indicate whether a given integer is prime or composite.
Formulae for Primes The formula of Jones, Sato, Wada and Wiens: the set of primes is the set of positive values taken by this expression.
Hardy-Littlewood Constants Infinite series over primes are the main topic in Hadamard-de la Vallée Poussin constants and in Brun's constant.
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.
K-Tuples Findings using an exhaustive search by Thomas J Engelsma.
Large Primes in Arithmetic Progression A repository maintained by Warut Roonguthai. One project is a search for six titanic primes in arithmetic progression.
Largest Known Primes Searchable database of these numbers. Lists largest primes by type and who discovered them.
New Primality Record E. Mayer and F. Morain announce that (2^7331-1)/458072843161 is prime. This number has 2196 decimal digits.
Prime Numbers and Factoring This page is a collection of links related to prime numbers and factoring of very large numbers.
Prime Numbers Directory A compilation of links related to prime numbers including primality tests, lists of prime numbers, factoring, Mersenne numbers and the Goldbach conjecture.
Prime Numbers List Browse all prime numbers of less than 10 digits. A prime number checker facility is also included.
Prime Records A compilation of records and resources by Jens Kruse Andersen.
PRIMES is in P. A paper by Manindra Agrawal, Neeraj Kayal, Nitin Saxena that presents a polynomal-time algorithm that determines whether an input number n is prime or composite [PS].
Proof of Bertrand's Postulate International Mathematics Olympiad tutorial proving the theorem of Chebyshef that there is a prime between n and 2n for all positive integers n > 1.
Pseudoprimes/Probable Primes Recent developments in primality testing. Here are slides of Jon Grantham's talk on this subject.
Radiant Primes Visualization of prime numbers resembling an astronomical radiant or celestial pathway.
Random Small Primes A site which gives some random primes up to 300 digits and more, also gives related information on primes.
Randomness and Prime Twin Proof A proof is offered by Martin Winer for the prime twin problem by defining randomness for a binary sequence.
Searching for Primes Illustrated Hypography article on how prime numbers are found, with reviewed links to prime number information.
Tables of Prime Numbers Lists of prime numbers to download in plain ASCII or MS-Excel format.
Testing for Primality Since ancient times, mathematicians have been fascinated by problems concerning prime numbers, and many people have worked on the problem of determining ways to test if numbers are prime. One way to test if a number is prime is to find the number's divisors. The following program finds the smallest integral divisor (greater than 1) of a given number n. It does this in a straightforward way, by testing n for divisibility by successive integers starting with 2.
The Distribution of the Primes Project Report on research into the 2nd Hardy-Littlewood conjecture and the relationship between the primes and chaotic systems by David O'Doherty. Includes program downloads.
The Prime Pages Prof. Chris Caldwell's database of virtually every large or otherwise interesting prime number known; includes the 5,000 largest known prime numbers and records for specific types.
