The Prime Puzzles & Problems Connection, by Carlos Rivera
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 ...
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Introductory prime number theory resources
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 ...
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Prime numbers
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 ...
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Aesthetics of the Prime Sequence
Number 7 Aesthetics of the Prime Sequence 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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Math Forum: Ask Dr. Math: FAQ
What is a prime number How can you find prime numbers What's the 'Sieve of Eratosthenes' What's the largest known prime
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Thomas R. Nicely's Home Page
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, ...
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Pulchritudinous primes - Visualizing the distribution of prime numbers...
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 ...
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Page of the Time traveler - A method of introducing irrational numbers to Classical numbers
PAGE OF THE TIME TRAVELER Has been awarded by Dr. Matrix on January 25, 1998 A new Theorem on Benford sets had been added on 26 may 2000 A new Theorem on Zeta functions had been added on 22 sept. 2000 ATTENTION ! May be best viewed by INTERNET EXPLORER 5.0 or HIGHER Dear reader , We are a Universal Organization joining the web from a Western Country (The name is not important ; as it may be ...
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Pseudoprimes/Probable Primes
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 ...
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Prime Numbers and Factoring
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 ...
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Introduction to Twin Primes and Brun's Constant
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 ...
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5.1 A Monte-Carlo Primality Tester.
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 ...
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Prime Patterns
Here are 45 prime number patterns. Included are; reversible primes, circular primes, prime pyramids, fortunate primes, depression primes, overlapping primes, etc.
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Example: Testing for Primality
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 ...
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Generalized Woodall Numbers
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 ...
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Carmichael numbers
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 ...
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Formulae for Primes
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 ...
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The Largest Known Primes
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 ...
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Brennen.Net Number Theory & Prime Links
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.
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Detecting False Reports In Primality Tests By The Oddcomp(z) Method
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 ...
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Prime
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 ...
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World records in computational number theory
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.
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Multifactorial Primes
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 ...
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Hardy-Littlewood Constants
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 ...
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