Dan Goldston

Daniel Goldston
Born	(1954-01-04) January 4, 1954 (age 63) Oakland, California
Nationality	American
Fields	Mathematics
Institutions	San Jose State University
Alma mater	UC Berkeley
Thesis	Large differences between consecutive prime numbers (1981)
Doctoral advisor	Russell Lehman
Known for	GPY theorem in number theory
Influenced	Yitang Zhang
Notable awards	Cole Prize (2014)

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. He has an Erdős number of 2.

Goldston is best known for the following result that he, János Pintz, and Cem Yıldırım proved in 2005:

where ${\displaystyle p_{n}\ }$ denotes the nth prime number. In other words, for every ${\displaystyle c>0\ }$, there exist infinitely many pairs of consecutive primes ${\displaystyle p_{n}\ }$ and ${\displaystyle p_{n+1}\ }$ which are closer to each other than the average distance between consecutive primes by a factor of ${\displaystyle c\ }$, i.e., ${\displaystyle p_{n+1}-p_{n}<c\log p_{n}\ }$.

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