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There are two related conjectures, each called the twin prime conjecture. The first version states that there are an infinite number of pairs of twin primes.
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Viggo Brun
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A second twin prime conjecture states that adding a correction proportional to to a computation of Brun's constant ending with will give an estimate with error less than. An extended form of this conjecture, sometimes called the strong twin prime conjecture or first Hardy-Littlewood conjecture, states that the number of twin primes less than or equal to x is asymptotically equal to where is the so-called twin primes constant. The value of is plotted above for, with indicated in blue. This conjecture is a special case of the more general k-tuple conjecture (also known as the first Hardy-Littlewood conjecture), which corresponds to the set.
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3000017 |
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