2/15/2006

Dan Goldston
San Jose State University

Small gaps between primes

I will describe recent joint work with Janos Pintz and Cem Yildirim on small gaps between primes. One surprising result is that if the primes are well distributed in arithmetic progressions then one can prove results not too far from the twin prime conjecture, for example, if the Elliott-Halberstam conjecture is true then there are infinitely many pairs of primes with difference 16 or less. Unconditionally we prove that there are pairs of primes much closer together than the average distance between consecutive primes.

This work has had its share of media attention, and even generated a song on public television. In my case there has been three stages to this publicity: the enjoyment of small-time public fame for proving the result two years ago, followed closely by the not so enjoyable publicity when the proof crashed, and lastly the redemption following the strange emergence of a new proof. After Wiles this may seem like standard procedure in mathematics, but I would not recommend it for the faint of heart.