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Sieving Prime Numbers From Thin Ore

Mathematicians have almost always been unable to take an infinite but sparsely distributed set of integers, such as the values of
 n + 1, and tell how rich in prime numbers it is, but now two mathematicians have developed powerful new techniques for assaying such "thin" subsets of integers for primes by refining a tool known as the asymptotic sieve. The new sieve shows that even though most numbers of the form
 a +
 b are composite--products of prime factors--the sequence includes an infinite number of primes.