Since 2 is the only even prime, this pair is the only pair of prime numbers that differ by one; thus twin primes are as closely spaced as possible for any other two primes | In other words, a twin prime is a prime that has a of two |
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This famous result, called , was the first use of the and helped initiate the development of modern | An empirical analysis of all prime pairs up to 4 |
As a result, the sum of any pair of twin primes other than 3 and 5 is divisible by 12.
53 as x tends to infinity | 7 for small x and decreases towards about 1 |
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Five is therefore the only prime that is part of two twin prime pairs | The work of in 2013, as well as work by , and others, has made substantial progress towards proving that there are infinitely many twin primes, but at present this remains unsolved |
There are 808,675,888,577,436 twin prime pairs below 10 18.
11The Encyclopedia of Integer Sequences | It was discovered in September 2016 |
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; ; 2009 , "Small gaps between primes or almost primes", Transactions of the American Mathematical Society 361 10 : 5285—5330, :• | The limiting value of f x is conjectured to equal twice the twin prime constant not to be confused with , according to the Hardy—Littlewood conjecture |
A stronger form of the twin prime conjecture, the Hardy—Littlewood conjecture see below , postulates a distribution law for twin primes akin to the.
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