| 1. | 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.
www.math.unicaen.fr |
| 2. | Prime Numbers and Factoring | | | This page is a collection of links related to prime numbers and factoring of very large numbers.
www.ontko.com |
| 3. | Prime k-tuplets | | | Tony Forbes' extensive collection of special types of prime clusters.
www.ltkz.demon.co.uk |
| 4. | The Prime Page | | | Methods and definitions of finding prime numbers.
www.fortunecity.com |
| 8. | Prime Constellations | | | Description of prime k-tuples, the first Hardy-Littlewood conjecture and the Hardy-Littlewood constants.
mathworld.wolfram.com |
| 10. | 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.
www-mitpress.mit.edu |
| 14. | 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.
www.bath.ac.uk |
| 16. | 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.
www.cs.bu.edu |
| 18. | Pseudoprimes/Probable Primes | | | Recent developments in primality testing. Here are slides of Jon Grantham's talk on this subject.
www.pseudoprime.com |
| 20. | The Time Traveler | | | A group with new propositions in various areas of number theory.
www.geocities.com |
| 22. | Patterns in Primes | | | Examples of digital patterns in prime numbers collected by Harvey Heinz.
www.geocities.com |
| 25. | Searching for Primes | | | Illustrated Hypography article on how prime numbers are found, with reviewed links to prime number information.
www.hypography.com |
| 26. | 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?
mathforum.org |
| 27. | World of Palindromic Primes | | | Records, statistics, and other interesting facts about palindromic primes compiled by Patrick De Geest.
www.worldofnumbers.com |
| 32. | 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.
ourworld.compuserve.com |
| 33. | Hardy-Littlewood Constants | | | Infinite series over primes are the main topic in Hadamard-de la Vallée Poussin constants and in Brun's constant.
pauillac.inria.fr |
| 35. | 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].
www.cse.iitk.ac.in |
| 36. | 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.
www.home.zonnet.nl |
| 39. | Number Spiral | | | Explains the number spiral, a method of visually representing the distribution of primes and the relationships between factors and products.
www.numberspiral.com |
| 40. | Radiant Primes | | | Visualization of prime numbers resembling an astronomical radiant or celestial pathway.
www.radiantprimes.com |
| 43. | 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.
odin.mdacc.tmc.edu |
| 44. | New Primality Record | | | E. Mayer and F. Morain announce that (2^7331-1)/458072843161 is prime. This number has 2196 decimal digits.
www.lix.polytechnique.fr |
| 46. | Prime Numbers List | | | Browse all prime numbers of less than 10 digits. A prime number checker facility is also included.
www.prime-numbers.org |
| 47. | K-Tuples | | | Findings using an exhaustive search by Thomas J Engelsma.
www.opertech.com |
| 48. | The Prime Machine | | | Explore interactively the Goldbach conjecture, the distribution of prime twins, the prime number theorem.
www.math.utah.edu |
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