| As a result, the sum of any pair of twin primes other than 3 and 5 is divisible by 12 | For example, 23 is an isolated prime, since 21 and 25 are both |
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| There are 808,675,888,577,436 twin prime pairs below 10 18 | The first few twin prime pairs are: 3, 5 , 5, 7 , 11, 13 , 17, 19 , 29, 31 , 41, 43 , 59, 61 , 71, 73 , 101, 103 , 107, 109 , 137, 139 , … |
of 58711-digit twin prime record• 2014 , "Variants of the Selberg sieve, and bounded intervals containing many primes", Research in the Mathematical Sciences 1: Art.
| Heini Halberstam, and Hans-Egon Richert, Sieve Methods, p | 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 |
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| ; ; 2009 , "Small gaps between primes or almost primes", Transactions of the American Mathematical Society 361 10 : 5285—5330, :• 3 as x tends to infinity |
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.
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