A List of Prime Numbers
All of the prime numbers less than 2000000000. |
A Monte-Carlo Primality Tester
The factoring problem seems very hard. But to test a number for having factors turns out to be much easier than to find them. It also helps if we supply the computer with a coin-flipping device. We now consider a Monte Carlo algorithm, i.e. one that with |
A Phyllotaxis Prime Number Sieve
A prime number sieve based on a daisy integer map. The sieving algorithm is demonstrated for a daisy with Fibonacci (21,34)-phyllotaxis using a three-dimensional diagram of a daisy capitulum and a two-dimensional spreadsheet. |
Aesthetics of the Prime Numbers Sequence
Prime visualizations (both visual and auditory), applets, message board, links. |
Applets for Prime Numbers
Factorization and weights of Proth coefficients. |
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. |
Detecting False Reports In Primality Tests By The Oddcomp(z) Method
Public-key algorithms need plenty of prime numbers. There are more primes than the number of atoms in the universe. All standing trees on planet Earth will not be sufficient to produce paper pulp to publish all the 512-bit primes in bound volumes. How do |
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. |
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. |
Entropy and Prime Numbers
Entropy of a nonnegative adjacency matrix related to prime numbers. |
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. |
Formulae for Primes
GIF images of a paper by A. Venugopalan in Proc. Indian Acad. Sci. (1983). |
Generalized Fermat Prime Search
Software, results and other resources. |
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. |
Introductory Prime Number Theory Resources
Notes and links compiled by Mark Watkins on the relation of the Riemann zeta function to the distribution of prime numbers. |
k-tuple Checker and Extender
Javascript program that checks for admissible prime k-tuples. |
Large Primes in Arithmetic Progression
Join the search for an example of 6 titanic primes in arithmetic progression. |
Multifactorial Primes
An organized search for primes of the form n!!!...!!!! +/-1. Includes table of numbers searched and primes found. |
New Primality Record
E. Mayer and F. Morain announce that (2^7331-1)/458072843161 is prime. This number has 2196 decimal digits. |
Notes and Literature on Prime Numbers
With applets to demonstrate properties of primes. |
Patterns in Primes
Examples of digital patterns in prime numbers collected by Harvey Heinz. |
Prime Constellations
Description of prime k-tuples, the first Hardy-Littlewood conjecture and the Hardy-Littlewood constants. |
Prime Number Generation
Notes on primality tests by Anuj Seth. |
Prime Number Records
By Paul Zimmermann. |
Prime Number Resources and Information
prime number basics |
Prime Number Spiral
Windows software exploring the prime number spiral. Online ordering. |
Prime Numbers
Historical topics about prime numbers. |
Prime Numbers
Largest known Mersenne primes. |
Prime Numbers and Factoring
This page is a collection of links related to prime numbers and factoring of very large numbers. |
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]. |
Problems of the Millenium: The Riemann Hypothesis
Description of the Riemann hypothesis by Enrico Bombieri discussing the problems history and significance, and the evidence to support the hypothesis. |
Pseudoprimes Based On Symmetric Functions
Basic propositions and computational techniques. |
Random Small Primes
A site which gives some random primes up to 300 digits and more , also gives related information on primes. |
Search of the Next Prime of the Form n!+1
The purpose of this page is to coordinate effort to search for the next prime of the form n!+1. At the moment our purpose is to search the range between 23,000!+1 - 30,000!+1. |
Searching for Primes
Illustrated Hypography article on how prime numbers are found, with reviewed links to prime number information. |
Some Results on the Number of Non-Witnesses to Compositeness
This paper introduces the reader to the Rabin-Miller probabilistic primality test, the concept of non-witnesses to compositeness, and the problem of determining the number of non-witnesses to compositeness. |
Tables of Prime Numbers
Lists of prime numbers to download in plain ASCII or MS-Excel format. |
The Largest Known Primes
An integer greater than one is called a prime number if its only positive divisors (factors) are one and itself. For example, the prime divisors of 10 are 2 and 5; and the first six primes are 2, 3, 5, 7,11 and 13. |
The New Book of Prime Number Records, Additions and Errata
Paulo Ribenboim has named this the "official" site for the collections of typos and errata from his text. |
The Nine and Ten Primes Project
The amazing story of the discovery of nine and finally ten consecutive primes in arithmetic progression. |
The Nth Prime Page
This online calculator finds the Nth prime, with N up to 10^12. It also finds the pi function (given a number, this function returns the number of primes below that number). |
The Prime Glossary
The award wining Prime Glossary has over 150 pages of definitions and terms related to prime numbers and factoring. |
The Prime Page
Methods and definitions of finding prime numbers. |
The Prime Page (An Index of Information on Prime Numbers)
The prime source for information about prime numbers! |
The Time Traveler
A group with new propositions in various areas of number theory. |
Twin Primes
Up to 10^14. |
Visualizing the Distribution of Prime Numbers
Investigation into patterns in the distribution of the primes by visualizing them. |
Wieferich Prime Number Search
A coordinated project to extend the list of Wieferich primes to 10^15. |
Wieferich Primes
Miscellaneous notes and graphics about Wieferich primes by Joe Crump. |
World of Palindromic Primes
Records, statistics, and other interesting facts about palindromic primes compiled by Patrick De Geest. |
World Records in Computational Number Theory
Record list for twin and Sophie Germaine primes. |
