Xkcd • Information 40 posts 21 authors - Last post Jul 31The twin prime conjecture simply states that there are an infinite number of twin primes. Twin primes are primes that have a difference of 2 http://echochamber.me/viewtopic.php?f=17&t=62848
MathFest 2007 In this talk I will discuss the method and why perhaps further progress towards bounded gaps and the twin prime conjecture is going to be difficult, http://www.certain.com/system/profile/web/index.cfm?pkwebid=0x66558d307
TWIN PRIME CONJECTURE - A VISIT TWIN PRIME CONJECTURE A VISIT. There is an identity which links the number of primes, twin primes and twin non-primes. This identity is based on the http://test.scoilnet.ie/Res/twin prime conjecture.htm
Extractions: TWIN PRIME CONJECTURE - A VISIT There is an identity which links the number of primes, twin primes and twin non-primes. This identity is based on the number of pairs of the form (6k-1, 6k+1) which exist within the Natural numbers. Thus i.e., Example: For n = 121 [n/6] = 20; PIo(n) = 1 (the pair (119,121));. PI(n) = 30 (the number of primes up to 121); PI2(n) = 10 (the number of twin prime pairs up to 121). Then 20 = 1 + 30 - 20 -1 Note: (119, 121) is the lowest occurrence of a twin non-prime Proof of the Identity For every increment of k by 1, [n/6] also increments by 1 - the Left Hand Side increments by 1. The next pair of the form (6k-1, 6k+1) must contain either 1 prime or 1 twin prime pair or 1 twin non-prime exclusively; ie. no two of these can occur together. Thus the Right Hand Side also increments by 1.
Prime Strings, Goldbach And His Evil Twin Jun 4, 2003 The Twin Prime Conjecture speculates that there is an infinite . The twin prime conjecture says that the string in row shift 2 does not 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:
Re Twin Primes Conjecture - Math Forum Discussions Re Twin Primes Conjecture Posted May 18, 2005 1102 AM The Twin Primes Conjecture (TPC) is quite obviously seen to be true if we http://mathforum.org/kb/thread.jspa?threadID=1141492&messageID=3773705
Twin Primes According to the (unsolved) twinprime conjecture there are infinitely many twin primes. The twin-prime conjecture generalizes to prime pairs that differ by http://www.daviddarling.info/encyclopedia/T/twin_primes.html
Extractions: In 1919 Brun showed that the sum of the reciprocals of the twin primes converges to a sum now known as Brun's constant : (1/3 + 1/5) + (1/5 + 1/7) + (1/11 + 1/13) + (1/17 + 1/19) + ... In 1994, by calculating the twin primes up to 10 , (and discovering the infamous Pentium bug in the process) Thomas Nicely of Lynchburg College estimated Brun's constant to be 1.902160578. According to the (unsolved) twin-prime conjecture there are infinitely many twin primes. The twin-prime conjecture generalizes to prime pairs that differ by any even number n , and generalizes even further to certain finite patterns of numbers separated by specified even differences. For example, the following triplets of primes all fit the pattern k k + 2, and k + 6: 5, 7, and 11; 11, 13, and 17; 17, 19, and 23; 41, 43, and 47. It is believed that for any such pattern not outlawed by divisibility considerations there are infinitely many examples. (The pattern k k + 2, and
Extractions: Current e-mail address Last revised 1000 GMT 18 January 2010. Date of first release 16 July 1999. The content of this document (other than the addendum, which was not part of the submission for publication) is essentially that of the original release, except that information rendered obsolete by subsequent events has been removed or modified, in both the main document and the addendum (this liberty is taken in view of the fact that the paper was never accepted for publication). There may also be differences in formatting, and in minor details and corrections, including updated URLs. Enumeration of the twin primes, and the sum of their reciprocals, is extended to 1.6e15. An improved estimate is obtained for Brun's constant, Error analysis is presented to support the contention that the stated error bound represents a 99 % confidence level. Primary: 11A41.
