Daniel Goldston
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Daniel Alan Goldston (born January 4, 1954 in Oakland, California) is an American mathematician who specializes in number theory. He is currently a professor of mathematics at San Jose State University.
Goldston is best known for the following result that he, János Pintz, and Cem Yildirim proved in 2005 [1]:
where 
denotes the nth prime number. In other words, for every 
, there exist infinitely many pairs of consecutive primes and 
which are closer to each other than the average distance between consecutive primes by a factor of 
, i.e., 
.
In fact, if they assume the Elliott-Halberstam conjecture, then they can also show that primes within 16 of each other occur infinitely often, which is nearly the twin prime conjecture.
