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	Prime number - Wikipedia, the free encyclopedia
		The prime number theorem says that the proportion of primes less than x is asymptotic to 1/ln x (in other words, as x gets very large, the likelihood that a number less than x is prime is inversely proportional to the number of digits in x).
		A probable prime is an integer which, by virtue of having passed a certain test, is considered to be probably prime.
		With this definition, the primes of the field Q of rational numbers are represented by the standard absolute value function (known as the "infinite prime") as well as by the p-adic valuations on Q, for every prime number p.
	en.wikipedia.org /wiki/Prime_number (3281 words)

	Prime pages - Wikipedia, the free encyclopedia
		The Prime pages is a website about prime numbers maintained by Prof.
		The list of the "5000 largest known primes" and lists of "top twenty" largest known primes of various interesting forms are maintained here.
		This page was last modified 15:16, 15 October 2005.
	en.wikipedia.org /wiki/Prime_pages (103 words)

	Illegal prime - Wikipedia, the free encyclopedia
		An illegal prime is a prime number which contains information forbidden by law to possess or distribute.
		The first illegal prime to be announced, when interpreted a particular way, describes a computer program which bypasses copyright protection schemes on some DVDs.
		The large prime database of the prime pages records the top 20 primes of various special forms; one of them is proof of primality using the elliptic curve primality proving (ECPP) algorithm.
	en.wikipedia.org /wiki/Illegal_prime (473 words)

	Machinery's Handbook MATH PAGES: Prime Numbers (Site not responding. Last check: 2007-10-20)
		Prime numbers in the tables are indicated by the letter P.
		If a number is not prime, the table gives the smallest factor by which the number is divisible.
		All even numbers are omitted from the tables because none are primes and all have a factor of 2.
	www.industrialpress.com /PrimeNumbers.htm (181 words)

	Will Edgington's Mersenne Page
		Prime exponent Mersenne numbers for which at least one LL test has been run and for which I have some factoring data but no factor are in DB.nf.
		The exponents of known Mersenne primes are in primeM.txt ; the complete factorizations known to me are in factoredM.txt (the largest prime factor is almost always implied, as some of them are _very_ large), and the roughly 6.7 MB lowM.txt contains the known information for all other Mersenne numbers with exponents less than 200,000.
		The status of Mersenne numbers with a Mersenne prime exponent (that is, M(M(p)) where M(p) = 2↑p - 1 is a Mersenne prime) is in MMPstats.txt.
	www.garlic.com /~wedgingt/mersenne.html (3423 words)

	Math Forum: Ask Dr. Math FAQ: Prime Numbers
		A prime number is a positive integer that has exactly two positive integer factors, 1 and itself.
		There is no largest prime number, but the effort to find ever-larger primes is ongoing and you can read about The Largest Known Primes on the Web.
		See Middle School Prime Numbers or search the Dr. Math archives using the words "prime number" (that exact phrase; just the words, not the quotes) to find questions and answers about prime numbers at all levels.
	mathforum.org /dr.math/faq/faq.prime.num.html (435 words)

	BBC NEWS \| Science/Nature \| Largest Prime Number discovered
		Mersenne primes are most relevant to number theory, but most participants join Gimps for the fun of having a role in real research - and the chance of finding a new Mersenne prime.
		The number 10 is not prime because it is divisible by 2 and 5.
		A Mersenne prime is a prime of the form 2^P-1.
	news.bbc.co.uk /2/hi/science/nature/3783149.stm (621 words)

	The Largest Known Primes
		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 problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic.
		Because the way the largest numbers N are proven prime is based on the factorizations of either N+1 or N-1, and for Mersennes the factorization of N+1 is as trivial as possible (a power of two).
	primes.utm.edu /largest.html (1149 words)

	Print Prime Numbers
		This page is sponsored by http://www.A-Wee-Bit-of-Ireland.com/ Your source in the USA for the finest Irish wool sweaters, celtic ruanas, capes, scarves and hats.
		He proved this by assuming that there were a finite number of primes and prime N was the biggest prime.
		This new number is not divisible by any of the primes that were multiplied together, therefore it is either a prime itself, or it is a product of a prime larger than the one we earlier assumed to be the largest prime.
	www.rsok.com /~jrm/printprimes.html (1044 words)

	The Prime Pages (prime number research, records and resources)
		Each of Webster's definitions may be applied to this page, but the most operative is 2a: An integer greater than one is prime if its only positive divisors are itself and one (otherwise it is composite).
		For example: 15 is composite because it has the two prime divisors 3 and 5.
		"Prime Curios!" is an exciting collection of curiosities, wonders and trivia related to prime numbers.
	primes.utm.edu (310 words)

	The Riesel Sieve Project (Site not responding. Last check: 2007-10-20)
		Early predictions said we would hit 12-15 primes in the 2^20 to 2^21 range....translated for some of you that is an n range between 1048576 and 2097152.
		Prime has been fully validated by numerous double checks and Prime Pages has officially verified it as prime.
		The prime must be in the form of k*2^n-1 and must be one of the 68 k's currently 'owned' by Riesel Sieve.
	www.rieselsieve.com (1075 words)

	New Scientist Breaking News - 7-million digit prime number discovered
		The largest prime number yet found has been discovered by a mathematics enthusiast using his desktop computer.
		Prime numbers are positive integers that can only be divided perfectly by themselves and one.
		A central server distributes different prime number candidates to each machine, which use spare processing power to test whether it is a genuine prime or not.
	www.newscientist.com /article.ns?id=dn5057 (430 words)

	BBC News \| SCI/TECH \| Number takes prime position (Site not responding. Last check: 2007-10-20)
		Mersenne primes are important for the theory of numbers and they may help in developing unbreakable codes and message encryptions.
		The first prime numbers are 2, 3, 5, 7, 11, etc. For example, the number 10 is not prime because it is divisible by 2 and 5
		It is the fifth, record prime found by the Gimps project, and the third discovered using a computing grid developed by Entropia.
	news.bbc.co.uk /hi/english/sci/tech/newsid_1693000/1693364.stm (802 words)

	Puzzle 131. Growing primes
		These primes are the matter of two articles (1, 2) of the well known glossary prime pages of Chris Caldwell, and was also part of the matter of an old puzzle in my pages.
		In the original definition you choose an initial prime that remains prime after cutting one digit at a time "by the right" until you reach to a one-digit prime.
		This is the point of view of a puzzle posted by Frank Rubin in his always interesting contest pages (The Contest Center).
	www.primepuzzles.net /puzzles/puzz_131.htm (414 words)

	Open Directory - Science: Math: Number Theory: Prime Numbers (Site not responding. Last check: 2007-10-20)
		Basic Theorems Concerning Prime Numbers - An introductory page on the theory of prime numbers with proofs of some important theorems including the infinitude of primes, Euclid's algorithm and the fundamental theorem of arithmetic.
		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.
		Prime Numbers and Factoring - This page is a collection of links related to prime numbers and factoring of very large numbers.
	dmoz.org /Science/Math/Number_Theory/Prime_Numbers (878 words)

	Prime pages -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-20)
		The Prime pages is a website about (An integer that has no integral factors but itself and 1) prime numbers maintained by Prof.
		Chris Caldwell at the (Click link for more info and facts about University of Tennessee) University of Tennessee at (Any of various swallows with squarish or slightly forked tail and long pointed wings; migrate around Martinmas) Martin.
		The site has a wealth of articles on primes and (Click link for more info and facts about primality testing) primality testing.
	www.absoluteastronomy.com /encyclopedia/p/pr/prime_pages.htm (134 words)

	Prime Facts
		Announced on December 7, 2001, in The Prime Pages.
		It was found by Michael Cameron with the Prime 95 prime- hunting program by George Woltman at the GIMPS site.
		Most recently, some researchers went as far as to compare groups of prime numbers in binary notation with biological sequences of DNA and RNA, and they were able to deduce by analogy that primes are not distributed at random but "that
	www.recoveredscience.com /Primes1ebook03.htm (1442 words)

	Illegal Prime Number?
		I have been a large prime prover (parse that either way!) for quite a while now (I refer you to, for example, the "Near Repdigit" record on Professor Caldwell's Prime Pages), and I tried to think how I could come up with a number archivable on those pages.
		The Prime Pages is the world's definitive resource for large prime number archiving and information; Professor Caldwell, who manages it, has put an awfully large amount of effort into deveoloping those pages, and into administering the archival of large primes, and has put a lot of thought into the criteria for their archivability.
		However it has become "interesting" enough to be one of the curios on the Prime Curios site, which is part of the Prime Pages site, and is for the more "fun" aspects of prime numbers.
	asdf.org /~fatphil/maths/illegal1.html (1435 words)

	The Math Forum - Math Library - Prime Numbers (Site not responding. Last check: 2007-10-20)
		An archive of primes, plus information on each prime, and on prime numbers in general, number systems, types of numbers, and universal constants.
		This is an introduction to Gaussian primes, complex numbers with integers for real and imaginary parts that are divisible by themselves and 1, but no other complex numbers with integer coefficients.
		The author of A Prime For The Millennium, in which is outlined his discovery of what he calls a 'millennium' prime, (a prime number with exactly 2000 digits), also provides links to a Fermat number record and the possiblity of a 6th Fermat prime.
	mathforum.org /library/topics/prime_numbers (2303 words)

	[No title]
		The previous record was 10^9999+33603 (10000 digits), proved prime using ECPP on August 19, 2003.
		The largest known twin primes are 33218925*2^169690+/-1 (51090 digits), found by Papp and Gallot in 2002.
		Sophie Germain primes P are such that P and 2P+1 are prime.
	www.loria.fr /~zimmerma/records/primes.html (644 words)

	The Top-20 Prime Gaps
		Proven primes are preferred here when practical, but prime gap searches usually produce PRP's which are not easily provable when the PRP is large.
		The average prime gap near an integer N is approximately ln N. The merit indicates the relative size of a prime gap, compared to the approximate average for that size primes.
		This page is based on an original page by Paul Leyland using partially different notation.
	hjem.get2net.dk /jka/math/primegaps/gaps20.htm (969 words)

	About The Prime Pages (Site not responding. Last check: 2007-10-20)
		The Prime Pages are a great place to learn everything you ever wanted to find out about prime numbers.
		Find out the definition of prime numbers, or browse the glossary for related terminology.
		Meet nice prime numbers in the "Prime Curios" collection of integer wonders and surprising trivia.
	www.learn.motion.com /topten/matlinks/PrimeP.htm (101 words)

	Primes R Us - Index (Site not responding. Last check: 2007-10-20)
		If you are just looking for all the prime numbers, I have posted files containing the first 5,800,000 prime numbers.
		This is a complete set of all primes from 2 through 100,711,433.
		If you are really interested in small primes and want more than a few million, you can download the program I used to create these.
	www.geocities.com /primes_r_us (372 words)

	Page Not Found!
		Sorry, but the page you are looking for is not available.
		The page you are looking for might have been removed, had its name changed, or is temporarily unavailable.
		If you reached this page by clicking a link, please contact us at info@superpages.com.my to alert us that the link is incorrectly formatted.
	www.superpages.com.my /primePages.do (118 words)

	College Mathematics Journal, The: Prime Pages, The (Site not responding. Last check: 2007-10-20)
		This prediction is based on a cubic regression of the logarithm of the number of digits of a record prime on the year found.
		The complete list of the record primes found since 1951, the first year that an electronic computer found one, shows that 24 of these 26 record primes are Mersenne primes.
		The website has links to many other websites such as one with the 5000 largest known primes, as well as the St. Andrews site (http://www-groups.dcs.st-and.ac.uk/history/HistTopics/Prime_numbers.html) where there is a nice general historical introduction to prime numbers.
	newssearch.looksmart.com /p/articles/mi_qa3773/is_200003/ai_n8884285 (357 words)

	Prime Curios!: Home Page
		This is an evolving collection at the Prime Pages; so we would be pleased to hear your opinions and suggestions.
		Our goal is to create a collection (a dictionary if you will) of individual prime numbers with interesting properties or forms.
		Since the number of primes is infinite, we can not list them all; but we can list the small ones that are especially curious.
	primes.utm.edu /curios (218 words)

	Radiant Prime
		Each prime number is converted to every base up to itself minus 1.
		Reversed, some numbers will form another prime number.
		The primes on the left start at 2 and continue down the page.
	www.radiantprimes.com (94 words)

	City Pages - Movies - Prime
		Like his young hero (Bryan Greenberg), who happens to be both the therapist's son and the client's rebound (unbeknownst to either woman), Younger proceeds a bit ambivalently into the kind of adulthood that can sometimes include the likes of Uma Thurman and Meryl Streep.
		Prime, named for the period of life enjoyed, sexually speaking, at different ages by woman (Thurman) and man (Greenberg), does a fairly amazing job of juggling the needs of both audiences as represented by the two lovers.
		No part of this service may be reproduced in any form without the express written permission of City Pages, Inc. except that an individual may download and/or forward articles via e-mail to a reasonable number of recipients for personal, non-commercial purposes.
	citypages.com /movies/detail.asp?MID=7357 (618 words)

	PrimeForm for Windows
		This page is dedicated to hosting PrimeForm, a primality-testing program for general mathematical expressions based on the wonderful mathematical libraries of Yves Gallot, used with his express permission under license.
		Special thanks go go Chris Caldwell, who now supports primes discovered by PrimeForm in his top 5000 database (at some considerable technical work on his "submit primes" pages!) and who also provided me with some intriguing code fragments that helped in the development.
		If you are seeking primes you may wish to use this to help you choose 'provable' forms.
	pages.prodigy.net /chris_nash/primeform.html (1814 words)

	The Mathematical Magic of the Fibonacci Numbers
		This page looks at some patterns in the Fibonacci numbers themselves, from the digits in the numbers to their factors and multiples and which are prime numbers.
		The first-index numbers seem to be either equal to the prime (as for p=5) or one less (as p=11) or 1 more (p=7) in many cases.
		The largest known Fibonacci prime, F(81839) was reported in April 2001 by David Broadbent and Bouk de Water.
	www.mcs.surrey.ac.uk /Personal/R.Knott/Fibonacci/fibmaths.html (12257 words)

	Thomas R. Nicely's Home Page
		Code written primarily in C, and distributed asynchronously across available personal computers running under extended DOS or Wndows, is employed to enumerate primes, prime* gaps, prime constellations (twins, triplets, and quadruplets) and their reciprocal sums (to extrapolate estimates for the corresponding Brun's constants).
		A supplemental table of the count of primes pi(x), with related functions, for some values of x between 5e15 and 5.9e15.
		An extensive table of pi_4(x), the count of prime quadruplets, with related functions, to 1.6e15.
	www.trnicely.net /index.html (2875 words)

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