
	Where results make sense

Topic: Twin prime

	Twin prime - Wikipedia, the free encyclopedia
		A twin prime is a prime number that differs from another prime number by two.
		A strong form of the twin prime conjecture, the Hardy-Littlewood conjecture, postulates a distribution law for twin primes akin to the prime number theorem.
		Every twin prime pair greater than 3 is of the form (6n - 1, 6n + 1) for some natural number n, and with the exception of n = 1, n must end in 0, 2, 3, 5, 7, or 8.
	en.wikipedia.org /wiki/Twin_prime (566 words)

	Twin prime conjecture - Wikipedia, the free encyclopedia
		The twin prime conjecture is a famous problem in number theory that involves prime numbers.
		Defining a Chen prime to be a prime p such that p + 2 is either a prime or a semiprime, Terence Tao and Ben Green showed in 2005 that there are infinitely many three term arithmetic progressions of Chen primes.
		Hardy and John Littlewood), which is concerned with the distribution of twin primes, in analogy to the prime number theorem.
	en.wikipedia.org /wiki/Twin_prime_conjecture (590 words)

	Twin prime (Site not responding. Last check: 2007-09-05)
		It is unknown whether there exist infinitely many twin primes, but most number theorists believe this to be true.
		It is known that the sum of the reciprocals of all twin primes converges (see Brun's constant).
		Every twin prime pair greater than 3 is of the form (6n - 1, 6n + 1) for some natural number n.
	bopedia.com /en/wikipedia/t/tw/twin_prime.html (246 words)

	Conjecture 3. Twin Prime's Conjecture
		This criterion R(k,a) recursively enumerate all prime k-tuples.
		As each further prime is cast out, a proportion of the u integers become m integers and the number of possible twin primes decreases.
		twin primes between a prime and its square, and since there are an infinite number of primes, there must be an infinite number of twin primes.
	www.primepuzzles.net /conjectures/conj_003.htm (3798 words)

	The Top Twenty: Twin Primes
		Twin primes are pairs of primes which differ by two.
		The first twin primes are {3,5}, {5,7}, {11,13} and {17,19}.
		Here the infinite product is the twin prime constant (estimated by Wrench and others to be approximately 0.6601618158...), and we introduce an integral to improve the quality of the estimate.
	primes.utm.edu /top20/page.php?id=1 (342 words)

	[No title]
		Twin Primes A twin prime is a prime number which differs from a given prime number by two.
		The twin prime method returns the number of twin primes which exist for a given number, as well as any the twin primes, should they exist.
		Number of Primes A method which finds the quantity of primes less than a given number is provided.
	www.physics.uci.edu /~smcmahon/readme.txt (1215 words)

	Prime Number Quadruplets 30 Apart, PNQ30, PIVCOM, 5TP39, Teapro
		Twin primes The simplest of these groups are called twin primes.They consist of two primes with a difference of 2, such as 11 and 13, or 29 and 31.
		The primes in each of these sets are separated by a composite number - one which is the product of two or more primes - which for want of a better name I call a pivotal composite, pivotal because it is the pivot of a symmetrical arrangement.
		It is well-known that all twin primes are of the form 6n-1 and 6n+1.
	www.teapro.com /datpnq30.html (2199 words)

	Math Forum - Ask Dr. Math
		Date: 3/11/96 at 15:19:1 From: KHU Subject: Twin prime numbers You know that a prime number is a whole number greater than 1 whose only whole number divisors are 1 and itself.
		These are pairs of prime numbers that are only 2 apart, such as 5 and 7, or 17 and 19, or 41 and 43.
		Experiment with some other pairs of twin primes, as well as with pairs of numbers that are not twin primes, and try to get some insight into what is happening.
	mathforum.org /library/drmath/view/55773.html (300 words)

	BBC NEWS \| Science/Nature \| Prime number breakthrough
		Primes can be multiplied to obtain all of the other integers.
		A curious observation is that primes occur in twins with a surprising regularity.
		The distribution of primes is closely related to one of the most renowned unsolved questions in mathematics, the Riemann hypothesis, which concerns an infinite sum of numbers called the zeta function.
	news.bbc.co.uk /1/hi/sci/tech/2911945.stm (583 words)

	Several Proofs of the Twin Primes Conjecture
		are not all the twin prime intervals, i.e.,
		Because all numbers n + k and n - k are not prime numbers, equations (2)-(4) are necessary for proving the infinitude but are not sufficient for finding the existence of prime numbers at these locations.
		However, since the number of twin primes is unlimited, their sum is an even number 2n unlimited and every sum of primes is an even number.
	www.coolissues.com /mathematics/Tprimes/tprimes.htm (508 words)

	PlanetMath: Germain prime
		It is conjectured that there are infinitely many Germain primes, but like the twin prime conjecture, this has not been proven.
		Cross-references: twin prime conjecture, twin prime constant, estimate, prime number
		This is version 2 of Germain prime, born on 2004-09-03, modified 2005-03-04.
	planetmath.org /encyclopedia/GermainPrime.html (71 words)

	NOVA \| scienceNOW \| Seven Prime Questions \| PBS
		A prime number is a number greater than one, a whole number whose only divisors—the only numbers that divide evenly into it—are itself and one.
		And whenever you have a pair of primes that differ by two, that's called a twin prime.
		And everyone believes there are infinitely many pairs of twin primes, but no one's been able to prove it.
	www.pbs.org /wgbh/nova/sciencenow/3302/02-numb-nf.html (727 words)

	[No title]
		In this well-written expository paper, the author surveys the history of prime number theory with an emphasis on the twin prime problem; in particular, there is a short biography with a photo of Viggo Brun, a pioneer in the study of this problem.
		The background is the enumeration of the number of twin primes up to $10\sp {14}$ and their reciprocal sum.
		The second result is an approximation to the conjecture of the existence of infinitely many twin primes and is apparently a new result.
	www.math.niu.edu /~rusin/known-math/99/twins (2106 words)

	TIPCO
		36 The smallest square that is the sum of a twin prime pair: 17 and 19.
		159 Its square (25281) is the concatenation of 2 primes: 2 and 5281.
		821 The smallest prime of the first prime quadruple for which the sums of the cubes of the digits of the 4 primes (821, 823, 827, 829) are primes themselves (521, 547, 863, 1249).
	www.trottermath.net /numthry/tipco.html (2511 words)

	[No title]
		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.
		Twin primes are primes of the form p and p+2, i.e., they differ by two.
		Altogether 37 of these primes are known, but since the region between the largest two and the previous primes has not been completely searched we do not know if the largest is 37th according to size.
	w3.impa.br /~gugu/mersenne/largest.txt (1308 words)

	American Institute of Mathematics (Site not responding. Last check: 2007-09-05)
		Number theorists moved a step closer to the resolving the twin prime conjecture this week when a new paper appeared on the internet, see the AIM preprint, which gives a proof that the spacing between consecutive primes is sometimes very much smaller than the average spacing.
		There is a belief among some number theorists that a psychological barrier has been broken and that a proof of the twin prime conjecture may not be far away.
		This work is a major step toward the centuries-old problem of showing that there are infinitely many "twin primes": prime numbers which differ by 2, such as 11 and 13, 17 and 19, 29 and 31,...
	aimath.org /primegaps (454 words)

	The Prime Glossary: twin prime
		It has been conjectured that there are infinitely many twin primes (see the twin prime conjecture for further information).
		Using sieve techniques, it has been proven that the sum of the reciprocals of the twin primes converge (see Brun's constant).
		It is trivial to show that other than the first pair, all pairs of twin primes have the form {6n-1, 6n+1}.
	primes.utm.edu /glossary/page.php?sort=TwinPrime (179 words)

	PlanetMath: twin prime conjecture
		Two consecutive odd numbers which are both prime are called twin primes, e.g.
		But is there an infinite number of twin primes ?
		This is version 7 of twin prime conjecture, born on 2003-01-07, modified 2005-04-21.
	planetmath.org /encyclopedia/TwinPrimeConstant.html (135 words)

	Math Trek: Closing the Gap on Twin Primes, Science News Online, July 16, 2005
		Primes often occur as pairs of consecutive odd integers: 3 and 5, 5 and 7, 11 and 13, 17 and 19, and so on.
		These so-called twin primes are scattered throughout the list of all prime numbers.
		The distribution of primes follows a remarkably simple pattern: The average spacing between primes near a number x is the natural logarithm of x, a number closely related to the number of digits in x.
	www.sciencenews.org /articles/20050716/mathtrek.asp (799 words)

	Ivars Peterson's MathTrek -Prime Twins
		Indeed, the twin prime conjecture is considered one of the major unsolved problems in number theory.
		Kelly and Pilling liken the numerical behavior of twin primes to that a radioactive substance, where the likelihood of one of its atoms decaying in any short time interval is fixed.
		Implications of a new characterization of the distribution of twin primes.
	www.maa.org /mathland/mathtrek_6_4_01.html (950 words)

	Thomas R. Nicely's Current Counts of Prime Constellaions (Site not responding. Last check: 2007-09-05)
		Stated below, for the present upper bound of the author's computations, are the count pi_4 of prime quadruplets (q, q+2, q+6, q+8); the partial sum S_4 of the reciprocals of the quadruplets; the resulting extrapolated estimate for the corresponding Brun's constant B_4; and an error estimate which the author conjectures to be definitive.
		For details of the error analysis, see the paper "Enumeration to 1.6e15 of the prime quadruplets"; further details will appear in the paper "Enumeration of the prime quadruplets (q, q+2, q+6, q+8)" (in preparation).
		Enumeration to 1.6e15 of the twin primes and Brun's constant (paper)
	www.trnicely.net /counts.html (240 words)

	Twin Primes Conjecture / Prime Sieve (Site not responding. Last check: 2007-09-05)
		Notes: At this point, all primes of this mathematical form are potentially twin, as each is spaced 2 apart from its nearest neighbor.
		There is one more thing that makes the twin prime sieve different from the regular prime sieve.
		The Twin Prime procedure takes these SAME branches, and pares off the ones that do not contain twin primes.
	members.aol.com /SciRealm/TwinPrimes.html (823 words)

	Twin Capital Management
		The TWIN Equity Model (TEM) is the “alpha engine” that drives our long-only equity products.
		We have been improving this dynamic, multi-factor stock selection model since TWIN opened its doors—providing it to other systematic equity managers early on.
		Prime has a higher tracking error than Active Equity, and seeks higher returns.
	www.twincapital.com /products_long_only.htm (182 words)

	Number Theory
		A Characterization of Twin Prime Pairs, (with Don H. Tucker).
		The basic idea of these remarks is to give a tight characterization of twin primes greater than three.
		It is hoped that this might lead to a decision on the conjecture that infinitely many twin prime pairs exist; that is, number pairs (p,p+2) in which both p and p+2 are prime integers.
	www.math.utah.edu /~gold/numbertheory.html (872 words)

	Twin prime conjecture proof
		The primes larger than the assumed "largest twin" are therefore more sparsely distributed than the smaller ones which unite their factor lines at that meeting level.
		Although the quantity of primes in the interval between the "largest twins" and the meeting of all smaller factor lines in a single space is higher than the number of primes up to those "largest twins",
		in the array to be hit by the factor line of a specific prime p is 1/p because it depends on how often that factor returns.
	www.recoveredscience.com /primes1ebook02.htm (1411 words)

	Page 012 (Site not responding. Last check: 2007-09-05)
		The twin prime conjecture and extensions of Chen's theorem
		from the d-twin prime conjecture of Hardy and Littlewood.
		Lavrik, On the twin prime hypothesis of the theory of primes
	www.math.utoledo.edu /~jevard/Page012.htm (1360 words)

	Open Directory - Science: Math: Number Theory: Prime Numbers (Site not responding. Last check: 2007-09-05)
		The Distribution of the Primes - Project Report on research into the 2nd Hardy-Littlewood conjecture and the relationship between the primes and chaotic systems by David O'Doherty.
		The Prime Machine - Explore interactively the Goldbach conjecture, the distribution of prime twins, the prime number theorem.
		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 (841 words)

	Table of contents
		The apex of the square- to- square "pyramid", and its strings of primes
		Patterns in the gaps between the primes of the triangular- number pyramid column at 7.
		Gaps between primes in the Euler Column under five, their composition from earlier primes, and their progression of "guest factors"
	www.recoveredscience.com /primes1content.htm (319 words)

	'Infinite Twin Primes' proof (?) : - GameDev.Net Discussion Forums
		Assume there is a greatest twin prime P. Then X = P + 1 is a prime number.
		Since Y is greater than P, Y is not a twin prime.
		A general note: a number p is considered to be a twin prime if p and p + 2 are prime, not p - 1 or p + 1.
	www.gamedev.net /community/forums/topic.asp?topic_id=288086 (1030 words)

	Counts of twin-prime pairs and Brun's constant to 5e15
		The values in this table were obtained by the author's direct and explicit generation and enumeration of the twin primes.
		The most extensive counts of pi_2(x) of which I am aware have been compiled by Tomás Oliveira e Silva (but do not include the values of the related functions delta_2(x), S_2(x), and F_2(x)).
		Symbols are defined as follows; for further details, see the papers A new error analysis for Brun's constant and Enumeration to 1.6e15 of the twin primes and Brun's constant.
	www.trnicely.net /twins/tabpi2.html (173 words)

Try your search on: Qwika (all wikis)