Surf these sites: 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 high probability rejects any composite number, but never a prime. A list of prime numbers -- All of the prime numbers less than 2000000000. A new primality record by E. Mayer and F. Morain -- We are glad to announce that MC7331=2^7331-1)/458072843161 is prime. This number has 2196 decimal digits and is the new record for general purpose primality proving (as far as we know). Aesthetics of the Prime Numbers Sequence -- My approach to the Prime-numbers is more intuitive than mathematical, but may worth to have a look. 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? Brief Findings From Primality Tests On (2^i+1) Family Of Sequences -- The number theoretic properties of the i^j+1 type of number sequences are investigated within the computing capabilities of a Pentium Pro PC. This paper reports briefly on some of the findings. Cryptography and coding theory with MAPLE page -- Some coding theory and cryptography links (most of which use MAPLE) 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 we detect false reports by probabilistic primality tests? EFF Cooperative Computing Awards -- Between $50,000 and $250,000 will go to the first individual or group who discovers a new prime number above 1 million digits. Finding Primes and Proving Primality (The quick tests) -- For finding all the small primes, say all those less than 10,000,000; the most efficient way is by using the Sieve of Eratosthenes (ca 240 BC) Finding primes and proving primality -- Starting with quick tests for small numbers, these pages describe how find prime and prove primality. We discuss probable-primes, the Lucas-Lehmer test for Mersennes, and most of the other classic theorems. 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. Generalization of Euler -Lagrange theorem -- It is possible to find a same result for p=1 [mod 4], with a new corresponding primality test, a generalization to Cunningham chains of second kind and primality tests of a new type ("in cluster"). Generalized Cunningham chains -- We call here "generalized Cunningham chains" the sequence of primes Pi such as Pi+1 = a*Pi+b, with a and b integers relatively prime. His length L is the number of successive primes in this sequence. Hardy-Littlewood Constants -- Infinite series over primes are the main topic in Hadamard-de la Vallée Poussin constants and in Brun''s constant. It''s About Prime -- capable of factoring numbers as large as 2^64 - 1 with the standard Macintosh Interface using our custom routines. Large Primes in Arithmetic Progression -- Join the search for an example of 6 titanic primes in arithmetic progression. Le théorème des nombres premiers -- article by François DRESS Links between prime numbers and physics -- Indirectly, as a result of studying nonlinear dynamics and chaos,Polish physicist Marek Wolf. Magic Stars of David (with Prime Numbers) -- A method , relating the creation of "David''s Star" ; by the utilization of prime numbers. Page of the Time traveler -- Some very interesting new theorems in various topics of numbers theory , which hasn''t been published till now. Perrin numbers -- Includes a Java Applet to compute Perrin numbers. Prime Number List -- This script generates a list of prime numbers. Once started, it will run until you click ''Stop'' Prime Number Resources and Information -- prime number basics Prime Numbers -- Largest known Mersenne primes Prime Numbers -- Mathematicians have a special fondness for definitions. The objects they study often have no physical presence: you can''t touch them, weigh them, or smell them. So, precise definitions are used to provide a solid underpinning to their subject. Prime Numbers and Factoring -- This page is a collection of links related to prime numbers and factoring of very large numbers. Prime k-tuplets -- Tony Forbes'' extensive collection of special types of prime clusters. Pseudoprimes/Probable Primes -- Recent Developments in Primality Testing, Here are slides of my talk on this subject. Publications of François Morain -- Thesis and papers on elliptic curves, especially primality proofs and point counting Random Small Primes -- A site which gives some random primes up to 300 digits and more , also gives related information on primes. Tables of Prime Numbers -- Lists of prime numbers to download in plain ASCII or MS-Excel format. Tech. History series (Prime numbers) -- We use computers for everything from writing letters to making music. It''s easy to forget that at their hearts, computers are number crunchers. In this Tech History report, Stan Bunger reports on how mathematicians did their work in the years BC -- before computers. 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 5000 largest known primes! -- This is the official page for the searchable database of the 5000 largest known primes--updated weekly! Do you want to know the largest prime, Mersenne, twin, Sophie Germain...? We start with the definition of prime and list many records. 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 Miller-Rabin Probabilistic Primality Test -- Why would we want a primality test that tells us the probability is 99.9999% that a number p is prime? For certain applications, as long as we have a very high probability that the number is prime, we can use that number for our purposes. 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 Prime Puzzles & Problems Connection -- Carlos Rivera''s collection of problems and puzzles related to prime numbers. The prime Glossary -- The elliptic curve primality proving algorithm (ECPP for short) 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. Timing tests on three primality test formulations. -- It is well known that whilst primality algorithms are extremely efficient when compared to brute force trial divisions, they yield probabilistic results meaning that there is a remote chance that one could find a counterexample. World of Palindromic Primes -- Records, stats, and other interesting facts about palindromic primes compiled by Patrick De Geest. Yves Gallot''s Proth.exe and Cunningham Chains -- A collection of interesting Cunningham chains plus how to find some with Yves Gallot''s Proth.exe.
Help build the largest human-edited
directory on the web.