# twin prime conjecture

Two consecutive odd numbers which are both prime are called , 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 $2n$. The case $n=1$ is the twin prime conjecture.

In 1940, Erdős showed that there is a constant $c<1$ and infinitely many primes $p$ such that $q-p where $q$ denotes the next prime after $p$. This result was improved in 1986 by Maier; he showed that a constant $c<0.25$ can be used. The constant $c$ is called the twin prime constant.

In 1966, Chen Jingrun showed that there are infinitely many primes $p$ such that $p+2$ is either a prime or a semiprime.

Title twin prime conjecture TwinPrimeConjecture 2013-03-22 13:21:32 2013-03-22 13:21:32 alozano (2414) alozano (2414) 11 alozano (2414) Conjecture msc 11N05 PrimeTriplesConjecture BrunsConstant twin prime constant twin primes