A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (17, 19) or (41, 43). 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.
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 (the so-called twin prime conjecture) or if there is a largest pair. The breakthrough[1]
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.[2]
Unsolved problem in mathematics:
Are there infinitely many twin primes?
(more unsolved problems in mathematics)
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Thomas, Kelly Devine (Summer 2014). "Yitang Zhang's spectacular mathematical journey". The Institute Letter. Princeton, NJ: Institute for Advanced Study – via ias.edu.
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Tao, Terry, Ph.D. (presenter) (7 October 2014). Small and large gaps between the primes (video lecture). UCLA Department of Mathematics – via YouTube.
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