1. Twin Primes Conjecture - Conservapedia The twin primes conjecture states that there are infinitely many twin primes. It is one of the great unsolved problems in mathematics, as it has never been proven. http://www.conservapedia.com/Twin_primes_conjecture

Twin primes conjecture From Conservapedia Jump to: navigation search The twin primes conjecture states that there are infinitely many twin primes . It is one of the great unsolved problems in mathematics , as it has never been proven. In 2004, Professor Arenstorf published a purported proof of this conjecture, but a fatal defect was discovered in the proof and the paper was retracted. In 1966, Chen Jingrun showed that there are infinitely many primes p such that p+2 is either a prime or the product of two primes (a " semiprime "), relying on a sieve theory. This resulted in defining a "Chen prime" to be a prime p such that p+2 is either a prime or a semiprime . In 2005, Ben Green and Terence Tao proved that there are infinitely many three-term arithmetic progressions of Chen primes. In 1915, Viggo Brun proved that the sum of reciprocals of the twin primes is convergent. This sum converges to Brun's constant Sources Math World Retrieved from " http://www.conservapedia.com/Twin_primes_conjecture Category Number Theory Views Page talk page View source History Personal tools Log in Search Popular Links Main Page Educational Index Debate Topics Recent changes ... Random page Help Help Index Statistics Conservapedia Commandments World History World History Lectures World History Homework Edit Console What links here Related changes Special pages Printable version ... Permanent link This page was last modified on 16 November 2008, at 07:37.

2. Several Proofs Of The Twin Primes Conjecture Goldbach s Conjecture proves and extends the Twin Primes Conjecture as probable. http://www.coolissues.com/mathematics/Tprimes/tprimes.htm

SEVERAL PROOFS OF THE TWIN PRIMES AND GOLDBACH CONJECTURES James Constant math@coolissues.com Proof of Goldbach's Conjecture, the Prime Number Theorem, and Euclid's Logic Provide Proofs of the Twin Primes Conjecture. Proof of the Twin Primes Conjecture Provides Proof of Goldbach's Conjecture Theorem There are infinitely many twin primes. Proof of the Twin Primes Conjecture Using Proofs of Goldbach's Conjecture or Using the Prime Number Theorem The twin primes conjecture (TPC) suggests that there is an infinite number of primes a and b with a difference , i.e., a - b = 2. Goldbach's conjecture (GC) suggests that every even number greater than is the sum s of two prime numbers a and b , i.e., a + b = s where s is even GC is proved by the author herein below and elsewhere For prime numbers a,b,c a - b = (a + c) - (b + c) even integer and thus, generally, a - b = 2k k = integer and since a + b is an even number a + b = 2n Now, using (2) and (3) results in a = n + k and b = n - k which say that for every single value of k primes a and b are separated by an interval and occur as numbers n + k and n - k . Suppose that n ,n ,n , . . . ,n

3. Twin Prime Conjecture -- From Wolfram MathWorld Oct 11, 2010 There are two related conjectures, each called the twin prime conjecture. The first version states that there are an infinite number of http://mathworld.wolfram.com/TwinPrimeConjecture.html

Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Unsolved Problems Twin Prime Conjecture There are two related conjectures, each called the twin prime conjecture. The first version states that there are an infinite number of pairs of twin primes (Guy 1994, p. 19). It is not known if there are an infinite number of such primes (Wells 1986, p. 41; Shanks 1993, p. 30), but it seems almost certain to be true. While Hardy and Wright (1979, p. 5) note that "the evidence, when examined in detail, appears to justify the conjecture," and Shanks (1993, p. 219) states even more strongly, "the evidence is overwhelming," Hardy and Wright also note that the proof or disproof of conjectures of this type "is at present beyond the resources of mathematics." Arenstorf (2004) published a purported proof of the conjecture (Weisstein 2004). Unfortunately, a serious error was found in the proof. As a result, the paper was retracted and the twin prime conjecture remains fully open. The conjecture that there are infinitely many Sophie Germain primes , i.e., primes

4. Bill The Lizard: Unsolved: Twin Primes Conjecture Jan 4, 2010 The Twin prime conjecture, which dates back to the 18th century, simply states that there are infinitely many twin primes. http://www.billthelizard.com/2010/01/unsolved-twin-primes-conjecture.html

skip to main skip to sidebar Bill the Lizard "The time has come," the Walrus said, "To talk of many things..." Monday, January 4, 2010 Unsolved: Twin Primes Conjecture Prime numbers, as most school children can tell you, are those numbers that are evenly divisible by only themselves and 1. The first few primes are We've known that there are infinitely many primes since c. 300 BC when it was proven by Euclid of Alexandria . Euclid used a very simple and elegant proof by contradiction. Euclid's proof of the infinitude of primes First, assume that there are a finite number of primes, p1, p2, p3, ..., pn. Now let Q = (p1 * p2 * ... * pn) + 1 That is, Q is equal to all of the primes multiplied together plus one. By the Fundamental Theorem of Arithmetic , Q is either prime or it can be written as the product of two or more primes. However, none of the primes in our list evenly divides Q. If any prime in our list did evenly divide Q, then that same prime would also evenly divide 1, since Q - (p1 * p2 * ... * pn) = 1 This contradicts the assumption that we had listed all the primes. So no matter how many primes we start with in our list, there must always be more primes. (Note that this proof does not claim that Q itself is prime, just that there must be some prime not in the initial list.)

5. Twin Prime - Wikipedia, The Free Encyclopedia A stronger form of the twin prime conjecture, the Hardy–Littlewood The twin prime conjecture would give a better approximation, as with the prime http://en.wikipedia.org/wiki/Twin_prime

Twin prime From Wikipedia, the free encyclopedia Jump to: navigation search A twin prime is a prime number that differs from another prime number by two . Except for the pair (2, 3), this is the smallest possible difference between two primes. Some examples of twin prime pairs are (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), ... (821, 823), etc. Sometimes the term twin prime is used for a pair of twin primes; an alternative name for this is prime twin Unsolved problems in mathematics Are there infinitely many twin primes? The question of whether there exist infinitely many twin primes has been one of the great open questions in number theory for many years. This is the content of the twin prime conjecture , which states There are infinitely many primes p such that p + 2 is also prime. In 1849 de Polignac made the more general conjecture that for every natural number k , there are infinitely many prime pairs p and p ′ such that p p k . The case k = 1 is the twin prime conjecture. A stronger form of the twin prime conjecture, the Hardy–Littlewood conjecture, postulates a distribution law for twin primes akin to the prime number theorem In 1915

6. Twin Prime - Wikipedia, The Free Encyclopedia A twin prime is a prime number that differs from another prime number by two. Except for the pair (2, 3), this is the smallest possible difference between two primes. http://en.wikipedia.org/wiki/Twin_prime_conjecture

Twin prime From Wikipedia, the free encyclopedia   (Redirected from Twin prime conjecture Jump to: navigation search A twin prime is a prime number that differs from another prime number by two . Except for the pair (2, 3), this is the smallest possible difference between two primes. Some examples of twin prime pairs are (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), ... (821, 823), etc. Sometimes the term twin prime is used for a pair of twin primes; an alternative name for this is prime twin Unsolved problems in mathematics Are there infinitely many twin primes? The question of whether there exist infinitely many twin primes has been one of the great open questions in number theory for many years. This is the content of the twin prime conjecture , which states There are infinitely many primes p such that p + 2 is also prime. In 1849 de Polignac made the more general conjecture that for every natural number k , there are infinitely many prime pairs p and p ′ such that p p k . The case k = 1 is the twin prime conjecture. A stronger form of the twin prime conjecture, the Hardy–Littlewood conjecture, postulates a distribution law for twin primes akin to the

7. Twin Primes My question is this When considering the Twin Primes Conjecture, has anyone researched the idea that (heuristically speaking) there is evidence that if p and p+2 are twin primes http://www.physicsforums.com/showthread.php?t=97958

8. CiteSeerX — Twin Primes Conjecture, 95 CiteSeerX Document Details (Isaac Councill, Lee Giles) solving linear congruences integer, 19 polynomial, 358 Sophie Germain prime, 94 splitting field, 364 square root http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1.2092

9. The Goldbach Conjecture NEXT The Twin Primes Conjecture . Interested? If you're interested in a positive discussion about everything the whole of protheory.com is mirrored on my Theory Of Everything Forum http://www.protheory.com/goldbach.html

Home Pro Theory Pro Answers Forum ... Discuss The Goldbach Conjecture The Goldbach Conjecture Introduction Every even number greater in size than 2 can be expressed as the sum of two primes. Conjecture This is one of the oldest unsolved problems in the field of mathematics and it concerns the patterns within prime numbers. Prime Prime numbers can only be evenly divided by themselves and 1. Simple The Goldbach Conjecture simply states that every even number greater in size than 2 can be expressed as the sum of two primes. Top of Page Verified Computer searches have apparently verified this conjecture up to 400 trillion, but a definite and singular proof or disproof continues to evade us. Summary Every even number greater in size than 2 can be expressed as the sum of two primes. Is this statement singularly provable? The Problem Can every even number greater than 2 be expressed unchangingly as the sum of two primes? The Answer Singular The answer to the Goldbach conjecture is that any singularly stated or singularly intended idea is missing its opposite and neutral potentials. Top of Page Unchanging The idea of a statement that can never change is theoretically inaccurate.

10. The Top Twenty: Twin Primes It has been conjectured (but never proven) that there are infinitely many twin primes. If the probability of a random integer n and the integer n+2 being http://primes.utm.edu/top20/page.php?id=1

11. Small Gaps Between Primes@Everything2.com What are the shortest intervals between consecutive prime number s? The twin primes conjecture, which asserts that P n+1P n =2 (where P n, as usual, stands for the N-th prime http://everything2.com/title/Small gaps between primes

Near Matches Ignore Exact Everything Small gaps between primes idea by Gartogg Tue Apr 15 2003 at 10:16:38 What are the shortest intervals between consecutive prime number s? The twin primes conjecture, which asserts that P n+1 -P n =2 (where P n , as usual, stands for the N-th prime ) infinitely often is one of the oldest problems; it is difficult to trace its origins. In the 1960's and 1970's sieve methods developed to the point where the great Chinese mathematician Chen was able to prove that for infinitely many primes P the number P+2 is either prime or a product of two primes. However the "parity problem" in sieve theory prevents further progress. What can actually be proven about small gaps between consecutive primes? A restatement of the prime number theorem is that the average size of P n+1 -P n is log(P n P n+1 -P n In 1926, Hardy and Littlewood, using their ``circle method'' proved that the Generalized Riemann Hypothesis (that neither the Riemann zeta function Riemann Hypothesis interval s contain a factor However, Dan Goldston and Cem Yildirim have recently written a manuscript (which was presented in a lecture at the

12. NOVA | Twin Prime Conjecture Jan 10, 2006 New insight into a 2300year-old mystery surrounding prime numbers inspires a song. http://www.pbs.org/wgbh/nova/physics/twin-prime.html

13. Math Forum Discussions his claims of having a proof of the Twin Primes Conjecture doing the same sketchy things that Riemann did to give you just some comprehension of the real math world. http://mathforum.org/kb/message.jspa?messageID=5383347&tstart=0

14. Twin Primes Conjecture Mathematical Games Up Unsolved Problems Previous Goldbach's conjecture. Twin primes conjecture. There exist an infinite number of positive integers p with p and p +2 both prime. http://www.cs.uwaterloo.ca/~alopez-o/math-faq/node63.html

Next: Mathematical Games Up: Unsolved Problems Previous: Goldbach's conjecture Twin primes conjecture There exist an infinite number of positive integers p with p and p +2 both prime. See the largest known twin prime section. There are some results on the estimated density of twin primes. Alex Lopez-Ortiz Mon Feb 23 16:26:48 EST 1998

15. Conjecture Famous conjectures include the Riemann hypothesis, the Poincar conjecture, the Goldbach conjecture, and the twin primes conjecture. http://www.daviddarling.info/encyclopedia/C/conjecture.html

16. Re: Twin Primes Conjecture At the least this discussion have given us a new heuristic principle, 'reductio ad quasiabsurdum' from the denial of a conjecture it can be deducted a proposition http://sci.tech-archive.net/Archive/sci.math/2005-05/msg03475.html

Re: Twin Primes Conjecture From Date : 18 May 2005 09:16:42 -0700 At the least this discussion have given us a new heuristic principle, that we can baptize as 'reductio ad quasi-absurdum': "If, from the denial of a conjecture it can be deducted a proposition that is much more harder to accept than the original, then the conjecture can be utilized as basis of an heuristic argument." Example: Conjecture:"The twin primes forms an infinite sequence" Its negation would convey to : The probalilistic formulas that give the quantity of twins approximate values, suddenly, from a number onwards begin to throw zeros. References Re: Twin Primes Conjecture From: luiroto Re: Twin Primes Conjecture From: Robert Israel Re: Twin Primes Conjecture From: luiroto Re: Twin Primes Conjecture From: Robert Israel Prev by Date: Re: How seriously do you take mathematics? Next by Date: Re: Orlow cardinality question Previous by thread: Re: Twin Primes Conjecture Next by thread: Re: Twin Primes Conjecture Index(es): Date Thread Relevant Pages Re: JSH: Understanding prime gaps issue a claim of having proven the Twin Primes Conjecture.

17. Math Horizon April 2007 Spoof On Shalosh B. Ekhad The spokescomputer offered a spectacular example We were able to prove the twinprimes conjecture simply by checking all positive integers. No human being can possibly do that http://www.math.rutgers.edu/~zeilberg/MathHorizons.html

Math Horizon April 2007 Spoof on Shalosh B. Ekhad [Appeared inside the article "Mathematical Enquirer (Volume 1 Issue 0, April 1, 2007)", pp. 17-20 of Math Horizons April 2007 issue. The article was written by Gary Gordon, Dan Kalman, Liz McMahon, Roger Nelsen, and Bruce Reznik] Electronic Journal of Computational Mathematics Launched The Atari Corporation announced a new research journal, exclusively devoted to articles written by computers, for computers. This journal fills a much needed gap in what current research journals offer. According to Shalosh B. Ekhad, spokescomputer for the new journal, "Computers have made tremendous advances in all fields of mathematics, in the past forty years. Humans are no longer necessary for the most important new research." The spokescomputer offered a spectacular example: "We were able to prove the twin-primes conjecture simply by checking all positive integers. No human being can possibly do that", it boasted. The journal, which will be edited by computers which have been discarded, is referred affectionately by its nickname 11235813. The editorial offices will be located beneath the Hackensack River bridge on the New Jersey Turnpike. The first volume, which occupies some 20,000 yottabytes, gives a "new" proof of the four-color theorem, eliminating any step that could possibly be checked by human beings. In a subsequent issue, the computers plan to give a "one-line solution" to the P. vs. NP problem (although the line will include an infinite loop).

18. PlanetMath: Twin Prime Conjecture Two consecutive odd numbers which are both prime are called twin primes, e.g. 5 and 7, or 41 and 43, or 1000000000061 and 1000000000063. http://planetmath.org/encyclopedia/TwinPrimesTheNumberOfConjuncture.html

(more info) Math for the people, by the people. donor list find out how Encyclopedia Requests ... Advanced search Login create new user name: pass: forget your password? Main Menu sections Encyclopædia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About twin prime conjecture (Conjecture) Two consecutive odd numbers which are both prime are called twin primes , e.g. 5 and 7, or 41 and 43, or 1,000,000,000,061 and 1,000,000,000,063. But is there an infinite number of twin primes ? In 1849 de Polignac made the more general conjecture that for every natural number $n$ there are infinitely many prime pairs which have a distance of The case $n=1$ is the twin prime conjecture. In 1940, Erdos showed that there is a constant and infinitely many primes $p$ such that where $q$ denotes the next prime after $p$ This result was improved in 1986 by Maier; he showed that a constant can be used. The constant $c$ is called the twin prime constant.

19. YouTube - Twin Primes Conjecture Song A song about twin primes conjecture http://www.youtube.com/watch?v=DSpKiJyJ9NI

20. Sci.math FAQ: Unsolved Problems * Collatz Problem * Goldbach's conjecture * Twin primes conjecture _ Names of large numbers http://www.uni-giessen.de/faq/archiv/sci-math-faq.unsolvedproblems/msg00000.html

Index sci.math FAQ: Unsolved Problems Subject : sci.math FAQ: Unsolved Problems From alopez-o@neumann.uwaterloo.ca (Alex Lopez-Ortiz) Date : Fri, 17 Nov 1995 17:15:13 GMT Newsgroups sci.math sci.answers news.answers Sender news@undergrad.math.uwaterloo.ca (news spool owner) Summary : Part 18 of many, New version, Index: Index sci-math-faq.unsolvedproblems

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