FastCounter by bCentral Search: in Primepuzzles.net Math World Prime Curios! Encyc. Int. Seq. (word) Encyc. Int. Seq. (sequence) Encyc. Int. Seq. (seq. num.) World!Of Numbers A new puzzle every Saturday. Solutions one week later. (Aug 10-16, 2002) Puzzle 189 Squares and primes in a row Latest News Wilke, Howell & Torasso and the Puzzle 188 Ken Wilke, Jim Howell and Flavio Torasso found - each ...

PrimeNet Lucas Lehmer 2nd PrimeNet Factoring 1st George's Top Producers 2nd How To Join Team Stats PrimeNet Report Mailing List Chat Room Forum Factored LL Tested P-1 Tested Trial Factored Other Ars Teams Ars Flying Squad Team Beef Roast Team Chili Pepper Team Crab Cake Team Egg Roll Team Frozen Yogurt Team Lamb Chop Team Primordial Soup Team Stir Fry Team Vodka Martini Our Friends Ars Technica ...

Introductory prime number theory resources the distribution of prime numbers (elementary, and visually-oriented presentation) the prime number theorem (proof outline and additional notes) Riemann's zeta function (links) the Riemann Hypothesis (links) D. Rockmore, Chance in the Primes This excellent and thorough article is intended as a commentary to supplement the first half of a popular talk on ...

Biography of Marin Mersenne (1588-1648) ...

Prime numbers Number theory index History Topics Index Prime numbers and their properties were first studied extensively by the ancient Greek mathematicians. The mathematicians of Pythagoras's school (500 BC to 300 BC) were interested in numbers for their mystical and numerological properties. They understood the idea of primality and were interested in perfect and amicable numbers. A perfect ...

Number 7&nbsp&nbsp&nbsp Aesthetics of the Prime Sequence&nbsp&nbsp&nbsp Main Introduction Primality testing applet Primes and music Primes and nucleotide bases Graphics Autism and primes Software Related Links Copyrights Message Board Security News Admin: atLab@a-tu.net Contemporary Research ...

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Palindromic (square, triangular, cube, prime, ...) Numbers and other Recreational Topics ...

Generalized Fermat Prime Search.

Hardy-Littlewood Constants The sequence of prime numbers has fascinated mathematicians for centuries. Consider, for example, the counting function It was not until 1896 that Hadamard and de la Vallee Poussin (building on the work of many) proved what is known as the Prime Number Theorem: For every problem that has been solved in prime number theory, however, there are several which remain ...

What is a prime number How can you find prime numbers What's the 'Sieve of Eratosthenes' What's the largest known prime

Some Results of Computational Research in Prime Numbers (Computational Number Theory) Thomas R. Nicely http://www.trnicely.net trnicely*hotmail.com E-mail security alert E-mail address display policy DESCRIPTION OF RESEARCH Code written primarily in C, and distributed asynchronously across available personal computers running under extended DOS or W*ndows, is employed to enumerate primes, ...

Upon looking at these numbers, one has the feeling of being in the presence of the inexplicable secrets of creation. D. Zagier from The first 50 million prime numbers . pul chri tu di nous; adj. Very pleasing or delightful to look at - Characterized by, or having great physical beauty and appeal. Introduction / Why Primes Visualizing Primes in 2D Visualizing Primes in 3D Prime Island! The Ulam ...

Mersenne Prime Digits and Names ...

Quick links to other Mersenne related files on my site M3status.txt: Data about factorization of M(p) - 2 for prime M(p). MMPstats.txt: Data about factorization of M(M(p)) for prime M(p). facntD.txt: Factor counts for completely factored M(n) for all n ...

Prime Constellation ...

Pseudoprimes/Probable Primes Recent Developments in Primality Testing Here are slides of my talk on this subject. The talk is contained in two separate files. talk0797.tex(16K) talk0797.dvi(20K) talk0797.ps (152K) talk0797.pdf (244K) talk0797a.tex(4K) talk0797a.dvi(4K) talk0797a.ps (50K) talk0797a.pdf (60K) Media Mentions The Spring 1997 issue of CryptoBytes, a newsletter of RSA Labs, contains ...

Prime Numbers and Factoring This page is a collection of links related to prime numbers and factoring of very large numbers. The Prime Page Chris K. Caldwell's page on primes, especially large ones, with lots of links to related information and software. Links to Sites Concerned with Prime Numbers and Number Theory, by Peter Meyer. You may also be interested in his Factorizer and Prime Number ...

The sieve of Eratosthenes, Prime Number, JavaScript, Faust-Gymnasium Staufen ...

Introduction to Twin Primes and Brun's Constant 1 Introduction It's a very old fact (Euclid 325-265 B.C., in Book IX of the Elements) that the set of primes is infinite and a much more recent and famous result (by Jacques Hadamard (1865-1963) and Charles-Jean de la Vallee Poussin (1866-1962)) that the density of primes is ruled by the law p(n) ~ n log(n) where the prime counting function p(n) is ...

Next: 5.2 Randomized Algorithms and Up: 5 Randomness in Computing. Previous: 5 Randomness in Computing. 5.1 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 list of prime numbers.

1.2.6 Example: Testing for Primality This section describes two methods for checking the primality of an integer n, one with order of growth , and a probabilistic algorithm with order of growth . The exercises at the end of this section suggest programming projects based on these algorithms. Searching for divisors Since ancient times, mathematicians have been fascinated by problems concerning ...

A Woodall number is a number of the form . A Woodall prime is any prime number of the same form. This notion can be generalized to numbers of the form where . The following is a list of generalized Woodall primes. Initially primes were discovered using the program Primeform, developed by Chris Nash and most primes below with an exponent less than 1000 are probable primes. Primality tests will be ...

Lucas Sequences in Cryptography This is a short note on the practical usefulness of Lucas sequences in applied cryptography. A Lucas sequence is a sequence of integers characterized by two parameters, P and Q. In practice Q is always 1 and the sequence is taken modulo a large integer. Calculating an element of a Lucas sequence is very similar to exponentiation. It may be helpful to think of P as ...

Primality testing with Fermat's little theorem If n is a prime, and 0 b n, then bn-1 is congruent to 1 modulo n. So if we compute bn-1 modulo n, and don't get 1, then we can conclude that n is not a prime. n = A number n is a pseudoprime to the base b if bn-1 is congruent to 1 modulo n. If a number is a pseudoprime to a variety of bases, then it is likely to be a prime. Below you can find out ...

Formulae for Primes Adrian Bowyer The set of prime numbers is identical with the set of positive values of as the variables range over the nonnegative integers. This seems superficially implausible because the expression is a product: the (k + 2) term at the start is multiplied by the expression in the curly brackets; but in fact all this means is that, when (k + 2) is not prime the second ...

The Largest Known Primes Contents: Introduction (What are primes Who cares ) The Top Ten Record Primes The Complete List of the Largest Known Primes Other Sources of Prime Information Notation and Definitions Euclid's Proof of the Infinitude of Primes Comments Suggestions New records New Links Related Local Documents: Finding (and Proving) Primes. Note: The most recent version of the ...

Least primitive root of prime numbers Least prime primitive root of prime numbers Least base necessary to prove the primality of a number Introduction Results References Links Contact Introduction Let p be a prime number. Fermat's little theorem states that a^(p-1) mod p=1 (a hat (^) denotes exponentiation) for all integers a between 1 and p-1. A primitive root of p is a number r such that any ...

Info & Applets for Number Theory & Prime Numbers All applets require a browser that supports version 1.1 of the Java AWT. If your browser fails to execute an applet, make sure you're running the latest version of the browser before reporting a bug A world record unitary aliquot sequence Applet - Compute weights of Proth coefficients Applet - Do factorization of numbers Feedback to jack@brennen.

Detecting False Reports In Primality Tests By The Oddcomp(z) Method by Huen Y.K. CAHRC, P.O.Box 1003, Singapore 911101 http://web.singnet.com.sg/~huens/ email: huens@mbox3.singnet.com.sg (A short communication - 1st released: 18/9/97. revision:20/9.) Abstract Public-key algorithms need plenty of prime numbers. There are more primes than the number of atoms in the universe . All standing trees on ...

The Prime Page: This is the wonderful prime number page, the page where I show you how little I know in a subject where theres lots to know. Also, don't expect an orderly presentation, for any knowledge I have comes in small bundles, and those bundles are not ordered. What is a Prime Number What's the problem How many are there Simple Qbasic program of mine to find them How do the big boys ...

World records in computational number theory Our joint work with Prof. Dr. Karl-Heinz Indlekofer in this field started in 1992. I worked in his research group from 1992 until 1997 as a project manager. During this period I designed most of the programs developed by the research group, coded and implemented approximately 70% of them. Record List A prime p is a twin prime if p+2 is prime as well.

Status of Search for Multifactorial Primes For information about multifactorial primes please see Chris Caldwell's glossary page on Multifactorial Primes and his list of the top 20 Primorial and Factorial Primes. Multifactorials are of the form forms n!!+/-1, n!!!+/-1, n!!!!+/-1 ... We shall call these 2-factorial plus or minus one, 3-factorial plus or minus one and so on. nmax tested Current ...

Mersenne and Fermat primes field Let NMF(b, p, n)= (b^(p^(n+1))-1)/(b^(p^n)-1) These numbers contain under the single general form the main remarkable numbers of number theory.Indeed, we obtains : - for b=2 and n=0 those are Mersenne's numbers. - for b=+/-2 et p=2 those are Fermat's numbers. - for b even and p=2 those are Generalized Fermat. - for b 2 and n=0 those are repunits base b. These ...

MERSENNE PRMES Nayan Hajratwala, George Woltman, Scott Kurowski, et. al. found the largest Mersenne Prime ever! It is 2^6972593-1. It is believed to be the 38th Mersenne Prime. It was found by a program by the Great Internet Mersenne Prime Search. My club, GIMPS, has the program, called Prime, or Prime 95, by George Woltman. Visit the mailing list of Mersenne Primes. P. S. If you don't want a ...