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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
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

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As a result, the sum of any pair of twin primes other than 3 and 5 is divisible by 12.

5
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-- A page of number theoretical constants• of 58711-digit twin prime record• Mathematical Sciences 82 4 : 61—65, : ,
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In other words, p is not part of a twin prime pair
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The University of Tennessee at Martin
3 as x tends to infinity 7 for small x and decreases towards about 1
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

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There are 808,675,888,577,436 twin prime pairs below 10 18.

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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 , …
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2001 , , , Kluwer Academic Publishers, ISBN 978-1556080104• The lower member of a pair is by definition a
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It follows from that primes are members of this sequence
The Encyclopedia of Integer Sequences It was discovered in September 2016
; ; 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

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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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يسمي كل عددين اوليين يكون الفرق بينهما 2 تواما اوليا فمثلا العددان 5،7 هما توام اولي اوجد جميع ازواج التوائم الاولية الاصغر من 50 ؟
For example, 23 is an isolated prime, since 21 and 25 are both
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Maynard, James 2015 , "Small gaps between primes", Annals of Mathematics, Second Series 181 1 : 383—413, :• 2014 , "Variants of the Selberg sieve, and bounded intervals containing many primes", Research in the Mathematical Sciences 1: Art
يسمي كل عددين اوليين يكون الفرق بينهما 2 تواما اوليا فمثلا العددان 5،7 هما توام اولي اوجد جميع ازواج التوائم الاولية الاصغر من 50 ؟
However, it is unknown whether there are infinitely many twin primes or there is a largest pair