What type of details about daniel goldston can be gathered from the following bio? Bio: daniel alan goldston -lrb- born january 4 , 1954 in oakland , california -rrb- 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 yldrm proved in 2005 : formula_1 where formula_2 denotes the nth prime number . in other words , for every formula_3 , there exist infinitely many pairs of consecutive primes formula_2 and formula_5 which are closer to each other than the average distance between consecutive primes by a factor of formula_6 , i.e. , formula_7 . this result was originally reported in 2003 by goldston and yldrm but was later retracted . then pintz joined the team and they completed the proof in 2005 . 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 related to the twin prime conjecture .
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