Research NewsMathematics

Sieving Prime Numbers From Thin Ore

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Science  02 Jan 1998:
Vol. 279, Issue 5347, pp. 31
DOI: 10.1126/science.279.5347.31

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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.