Twin Primes Definition

A twin prime is a prime number that is either 2 less or 2 more than another prime number. For instance, either member of the twin prime pair 41 and 43. Other examples include 3 and 5, 11 and 13, 17 and 19. In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term twin prime is used for a pair of twin primes. An alternative name for this is prime twin or prime pair.

Overview

Twin primes become increasingly rare as one examines larger ranges, in keeping with the general tendency of gaps between adjacent primes to become larger as the numbers themselves get larger. However, it is unknown whether there are infinitely many twin primes or there is a largest pair. The work of Yitang Zhang in 2013, as well as work by James Maynard, Terence Tao and others, has made substantial progress towards proving that there are infinitely many twin primes, but at present this remains unsolved.