Web Resources Guide For Chapter 3 sieve of Eratosthenes and for exploring the distribution of prime numbers.Information about twin primes and the Goldbach conjecture is also provided. http://www.mhhe.com/math/advmath/rosen/r5/student/ch03/weblinks.html
Extractions: Information Center Instructor Center Student Center Home Student Center Interactive Demos Self Assessments A Guide to Writing Proofs Common Mistakes in Discrete Math ... Bulletin Board Chapter Level Resources Choose one ... Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Web Resources Guide Maple Supplement Extra Examples Extra Steps Discrete Mathematics and Its Applications Guidance on how to write proofs as well as an introduction to proof strategies, can be found at Larry W. Cusick's website. Go to How To Write Proofs: http://zimmer.csufresno.edu/~larryc/proofs/proofs.html Another website with more information on several different methods of proof can be found at Proving Real Theorems: http://cse.stanford.edu/classes/cs103a/h24RProofs.htm An interesting variety of proofs and other problems in mathematics can be found at the Cut-the-Knot site. Proofs in Mathematics: http://www.cut-the-knot.com/proofs/index.shtml A selection of proofs by contradiction can be found at Proofs by Contradiction: http://zimmer.csufresno.edu/~larryc/proofs/proofs.contradict.html
Science -- Sign In No one knows whether twin primes ever stop appearing. The new proof is still afar cry from the twin prime conjecture, but it offers a glimmer of hope that http://www.sciencemag.org/cgi/content/full/308/5726/1238
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::MHC Math Club: PROBLEM Of The WEEK:: Note This problem is related to the twin prime conjecture. This is the conjecturethat there are infinitely many pairs of twin primes. twin primes are http://www.mtholyoke.edu/~ysasanne/math/mathclubproblem.html
Extractions: Problem of the Week #8 (November 29) Given a segment AB in the plane and a line L in the same plane, let n(L) be the number of points C on L such that triangle ABC is isosceles. For example, I L is the perpendicular bisector of AB, then n(L)= infinity. What are the other possible values of n(L)? And how do they occur? You are a sales representative for a company based in Delaware. Your boss gives you a new assignment: you have to drive to the company's office in each of the 48 contiguous states, beginning from Delaware. The catch is that you can only enter each state once. While you are sitting at your desk trying to figure out how to do this, the company CEO stops by your cubicle.
Proof Of Golbach S Conjecture And The Twin Prime Conjecture Proof of Golbach s conjecture and the twin prime conjecture He s also proven twin primes, Riemann hypothesis, and of course Fermat s Last Theorem. http://www.physicsforums.com/archive/t-81643_Proof_of_Golbach's_conjecture_and_t
Extractions: This is not a proof, there are multiple mistakes and they have neglected to prove some areas which I believe to be untrue anyway. I need to head off to the shop, I might sit down later and try and demonstrate why this isn't true unless someone else has either done this or in fact shown me to be wrong. Discuss Proof of Golbach's conjecture and the twin prime conjecture Here, Free!
Extractions: Week of July 16, 2005; Vol. 168, No. 3 Ivars Peterson B.C. ) provided a simple proof that the sequence of prime numbers continues forever. A prime is a whole number (other than 1) that's evenly divisible only by itself and 1. This definition leads to the following sequence of numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, and so on. Suppose there is a finite number of primes, Euclid argued. This means there's also a largest prime, n . Multiply all the primes together, then add 1: (2 x 3 x . . . x n ) + 1. The new number is certainly bigger than the largest prime. If the initial assumption is correct, the new number can't be a prime. Otherwise, it would be the largest. Hence, it must be a composite number and divisible by a smaller number. However, because of the way the number was constructed, any known prime, when divided into the new number, leaves a remainder of 1. Therefore, the initial assumption can't be correct, and there can be no largest prime. 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. However, there's no proof yet that there are infinitely many pairs of primes that differ by only 2.
Professeur Badih GHUSAYNI The twin prime conjecture states that the number of twin primes is infinite. The objective of this note is to tie the twin prime conjecture to complex http://www.ul.edu.lb/francais/publ/ghus.htm
CJM - Primes In Short Segments Of Arithmetic Progressions Assuming a strong form of the twin prime conjecture and the Riemann Hypothesisone can obtain an asymptotic formula for the total variance in the range when http://www.journals.cms.math.ca/cgi-bin/vault/view/goldston0874
Goldbach Conjecture Verification The Goldbach conjecture is one of the oldest unsolved problems in number theory 1, is the twin primes constant. In 3, Crandall and Pomerance suggest http://www.ieeta.pt/~tos/goldbach.html
Extractions: Introduction News Results Top 20 ... [Up] The Goldbach conjecture is one of the oldest unsolved problems in number theory [1, problem C1] . In its modern form, it states that every even number larger than two can be expressed as a sum of two prime numbers. Let n be an even number larger than two, and let n=p+q , with p and q prime numbers, , be a Goldbach partition of n . Let r(n) be the number of Goldbach partitions of n . The number of ways of writing n as a sum of two prime numbers, when the order of the two primes is important, is thus R(n)=2r(n) when n/2 is not a prime and is R(n)=2r(n)-1 when n/2 is a prime. The Goldbach conjecture states that , or, equivalently, that , for every even n larger than two. In their famous memoir [2, conjecture A] , Hardy and Littlewood conjectured that when n tends to infinity, R(n) tends asymptotically to (i.e., the ratio of the two functions tends to one) n p-1 N2(n) = 2 C PRODUCT - , twin (log n)(log n-2) p odd prime p-2 divisor of n where p(p-2) C = PRODUCT - = twin p odd prime (p-1)^2 is the twin primes constant. In
Twin Prime Conjecture -- From MathWorld There are two related conjectures, each called the twin prime conjecture. As a result, the paper was retracted and the twin prime conjecture remains http://mathworld.wolfram.com/TwinPrimeConjecture.html
Extractions: MATHWORLD - IN PRINT Order book from Amazon Number Theory Prime Numbers Prime Clusters ... 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 Top Twenty: Twin Primes In 1919 Brun showed that the sum of the reciprocals of the twin primes converges to Two HardyLittlewood Conjectures; The Prime Glossary s twin primes http://primes.utm.edu/top20/page.php?id=1
Twin Prime Conjecture - Wikipedia, The Free Encyclopedia The twin prime conjecture is a famous problem in number theory that involvesprime numbers. There is also a generalization of the twin prime conjecture, http://en.wikipedia.org/wiki/Twin_Prime_Conjecture
Extractions: (Redirected from Twin Prime Conjecture The twin prime conjecture is a famous problem in number theory that involves prime numbers . It states: There are an infinite number of primes p such that p Such a pair of prime numbers is called a twin prime . The conjecture has been researched by many number theorists. Mathematicians believe the conjecture to be true, based only on numerical evidence and heuristic reasoning involving the probabilistic distribution of primes. In de Polignac made the more general conjecture that for every natural number k , there are infinitely many prime pairs which have a distance of 2 k . The case k edit In Viggo Brun showed that the sum of reciprocals of the twin primes was convergent. This famous result was the first use of the Brun sieve and helped initiate the development of modern sieve theory . The modern version of Brun's argument can be used to show that the number of twin primes less than N does not exceed C N / log N for some absolute constant In Paul ErdÅs showed that there is a constant c p such that p p c p , where p ' denotes the next prime after p . This result was successively improved; in
Goldbach's Conjecture - Wikipedia, The Free Encyclopedia The strong Goldbach conjecture is in fact very similar to the twin prime conjecture,and the two conjectures are believed to be of roughly comparable http://en.wikipedia.org/wiki/Goldbach's_conjecture
Extractions: In mathematics, Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics . It states: For example, edit In , the Prussian mathematician Christian Goldbach wrote a letter to Leonhard Euler in which he proposed the following conjecture: He considered 1 to be a prime number , a convention subsequently abandoned. So today, Goldbach's original conjecture would be written: Euler, becoming interested in the problem, answered with an equivalent version of the conjecture: The former conjecture is today known as the "ternary" Goldbach conjecture, the latter as the "strong" Goldbach conjecture. The conjecture that all odd numbers greater than 9 are the sum of three odd primes is called the "weak" Goldbach conjecture. Both questions have remained unsolved ever since, although the weak form of the conjecture is much closer to resolution than the strong one. edit The majority of mathematicians believe the conjecture (in both the weak and strong forms) to be true, at least for
Twin Prime Conjecture -- Facts, Info, And Encyclopedia Article twin prime conjecture. Categories conjectures, Number theory, The twinprime conjecture is a famous problem in (Click link for more info and facts http://www.absoluteastronomy.com/encyclopedia/t/tw/twin_prime_conjecture.htm
Extractions: In 1849 (Click link for more info and facts about de Polignac) de Polignac made the more general conjecture that for every natural number k , there are infinitely many prime pairs which have a distance of 2 k . The case k = 1 is the twin prime conjecture. In 1915, (Click link for more info and facts about Viggo Brun) Viggo Brun showed that the sum of reciprocals of the twin primes was convergent. This famous result was the first use of the Brun sieve and helped initiate the development of modern
Twin Prime -- Facts, Info, And Encyclopedia Article A strong form of the twin Prime conjecture, the (Click link for more info and The limiting value of f(x) is conjectured to equal the twin prime constant http://www.absoluteastronomy.com/encyclopedia/t/tw/twin_prime.htm
Extractions: A twin prime is a (An integer that has no integral factors but itself and 1) prime number that differs from another prime number by (The cardinal number that is the sum of one and one or a numeral representing this number) two . Except for the pair (2, 3), this is the smallest possible difference between two primes. Some examples of twin prime pairs are 5 and 7, 11 and 13, and 821 and 823. (Sometimes the term twin prime is used for a pair of twin primes; an alternative name for this is prime twin The question of whether there exist infinitely many twin primes has been one of the great open questions in (Click link for more info and facts about number theory) number theory for many years. This is the content of the (Click link for more info and facts about Twin Prime Conjecture) Twin Prime Conjecture . A strong form of the Twin Prime Conjecture, the (Click link for more info and facts about Hardy-Littlewood conjecture) Hardy-Littlewood conjecture , postulates a distribution law for twin primes akin to the (Click link for more info and facts about prime number theorem) prime number theorem Using his celebrated (Click link for more info and facts about sieve method) sieve method (Click link for more info and facts about Viggo Brun) Viggo Brun shows that the number of twin primes less than x is sum of the (Something (a term or expression or concept) that has a reciprocal relation to something else)
PlanetMath: Twin Prime Conjecture The case $ n=1$ is the twin prime conjecture. twin prime conjecture isowned by alozano. full author list (2) owner history (1) http://planetmath.org/encyclopedia/TwinPrimeConstant.html
Extractions: 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 , there are infinitely many prime pairs which have a distance of . The case is the twin prime conjecture. constant and infinitely many primes such that where denotes the next prime after . This result was improved in 1986 by Maier; he showed that a constant can be used. The constant is called the twin prime constant. In 1966, Chen Jingrun showed that there are infinitely many primes such that is either a prime or a semiprime
Extractions: Culture Geography History Life ... WorldVillage (Redirected from Twin Prime Conjecture The twin prime conjecture is a famous problem in number theory that involves prime numbers . It states: There are an infinite number of primes p such that p Such a pair of prime numbers is called a twin prime . The conjecture has been researched by many number theorists. Mathematicians believe the conjecture to be true, based only on numerical evidence and heuristic reasoning involving the probabilistic distribution of primes. In de Polignac made the more general conjecture that for every natural number k , there are infinitely many prime pairs which have a distance of 2 k . The case k Contents 1 Partial results edit In Viggo Brun showed that the sum of reciprocals of the twin primes was convergent. This famous result was the first use of the Brun sieve and helped initiate the development of modern sieve theory . The modern version of Brun's argument can be used to show that the number of twin primes less than N does not exceed C N / log N for some absolute constant In showed that there is a constant c p such that p p c p , where p ' denotes the next prime after p . This result was successively improved; in
Conjecture 3. Twin Prime's Conjecture This is the twin prime conjecture , which can be paraphrased this way Thereare infinite in the proof twin prime conjecture and so on, publish it. http://www.primepuzzles.net/conjectures/conj_003.htm
Extractions: Conjectures Conjecture 3. Twin Prime's Conjecture If we define d n as : d n = p n+1 - p n , is easy to see that d =1 and d n Now, that " for n>1, dn=2 infinitely often" (Ref. 2, p. 19). This is the "Twin prime Conjecture", which can be paraphrased this way : "There are infinite consecutive primes differing by 2". SOLUTION Mr Liu Fengsui has sent (3/9/01) an argument that proves - according to him - the well known and named " k-tuple conjecture " This conjecture can be expressed the following way (see Therefore, if this the Mr Liu's argument is correct then also the Twin Primes conjecture has been proved. As you soon will discover this argument is close related to the Liu's approach to the prime numbers definition, approach that has been exposed in detail in the Problem 37 of these pages. What follows is Mr Liu's argument. I should strongly point out that the most that Mr. Liu
Twin Prime Conjecture Encyclopedia twin prime conjecture. The twin prime conjecture is a famousproblem in number theory that involves prime numbers. It states http://encyclopedie-en.snyke.com/articles/twin_prime_conjecture.html
Extractions: The twin prime conjecture is a famous problem in number theory that involves prime numbers . It states: There are an infinite number of primes p such that p + 2 is also prime. Such a pair of prime numbers is called a twin prime . The conjecture has been researched by many number theorists. Mathematicians believe the conjecture to be true, based only on numerical evidence and heuristic reasoning involving the probabilistic distribution of primes. In de Polignac made the more general conjecture that for every natural number k , there are infinitely many prime pairs which have a distance of 2 k . The case k = 1 is the twin prime conjecture. Contents 1 Partial results 5 External links In Viggo Brun showed that the sum of reciprocals of the twin primes was convergent. This famous result was the first use of the Brun sieve and helped initiate the development of modern sieve theory . The modern version of Brun's argument can be used to show that the number of twin primes less than N does not exceed C N / log N for some absolute constant In showed that there is a constant c p such that p p c ln p , where p ' denotes the next prime after p . This result was successively improved; in
Extractions: Of course you could also skip the article and just look at the preprint on arxiv here Update [2004-6-10 13:39:44 by overconvergent]: The preprint has been withdrawn from the arXiv; because: A serious error has been found in the paper, specifically, Lemma 8 is incorrect. Post a Comment Unions Considered Harmful? New Largest Prime Number Found (0 comments) Display: Threaded Minimal Nested Flat Sort: Unrated, then Highest Highest Rated First Lowest Rated First Ignore Ratings Newest First Oldest First Twin Prime Conjecture Proven? comments (3 topical, 1 editorial, hidden) [new] There seems to be some doubt emerging ...
Prime Strings, Goldbach And His Evil Twin Essentially, the twin prime conjecture stipulates that the binary string created The twin prime conjecture states that binary row in the first row is an http://descmath.com/prime/prime_strings.html
Extractions: The two most famous mathematical conjectures concerning primes are: The Twin Prime Conjecture and the Goldbach Conjecture. The Twin Prime Conjecture speculates that there is an infinite number of primes pairs p1 and p2 such that (p2 - p1 = 2). The Goldbach Conjecture stipulates that all even numbers can be written as the sum of two primes. I am inclined to believe that both conjectures are true. But, like most proofs that involve establishing a truth for an infinite collection, the postulates are devilishly difficult to prove. I've found that representing the primes with a binary string, makes it is easy to see the relation between the Goldbach and Twin Prime conjectures. A binary string is simply a long string of boolean characters. A boolean character has only two possible values. The boolean value is either on or off, true or false. Computer programmers often express binary strings as a series of 1s and 0s. To represent the primes as a binary string, I simply look at each number starting with 1. If the number is prime, I record a "1". If not, I record "0". The nth value in this binary string will be 1 if n is prime, else 0. When discussing the Twin Prime and Goldbach conjectures, I find it easiest to drop the even numbers. To create a binary string that represents the odd integers, I start with a list of dds then record if it is prime:
