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Short Summaries of Articles about Mathematics in the Popular Press

"Sieving Prime Numbers from Thin Ore," by Barry Cipra. Science, 2January 1998, page 31.

This article describes a recent breakthrough by number theorists inunderstanding the density of primes in infinite sequences of numbers. Givenany sequence of numbers, such as numbers of the form n^{2} + 1, where nis a whole number, it is extremely difficult to tell how many primes thesequence contains. Mathematicians John Friedlander and Henryk Iwaniec haveestablished that the sequence of numbers of the form a^{2} +b^{4} contains infintely many primes. This represents the firstsubstantial progress on this question in about a century. Number theorists arealso lauding the ingenious techniques used in the Friedlander-Iwaniec work.