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, Janos Pintz, and Cem Yildirim proved in 2005 ^*:

$\backslash liminf\_\{n\backslash to\backslash infty\}\backslash frac\{p\_\{n+1\}-p\_n\}\{\backslash log\; p\_n\}=0$

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

See also

• Dan Goldston's Homepage

American mathematicians | 20th century mathematicians | 1954 births | Living people | San José State University