# Cem Yıldırım

Cem Yalçın Yıldırım
BornJune 8, 1961 (age 58)
NationalityTurkish
CitizenshipRepublic of Turkey
Alma materMiddle East Technical University (BSc, 1982)
University of Toronto (PhD, 1990)
AwardsCole Prize (2014)
Scientific career
FieldsMathematics
InstitutionsBilkent University
Bogazici University
Websitemath.boun.edu.tr/../yildirim.htm

Cem Yalçın Yıldırım (born 8 July 1961)[1] is a Turkish mathematician who specializes in number theory. He obtained his B.Sc from Middle East Technical University in Ankara, Turkey and his PhD from the University of Toronto in 1990.[2] His advisor was John Friedlander. He is currently a faculty member at Boğaziçi University in Istanbul, Turkey.

In 2005([3]), with Dan Goldston and János Pintz, he proved, that for any positive number ε there exist primes p and p′ such that the difference between p and p′ is smaller than ε log p.

Formally;

${\displaystyle \liminf _{n\to \infty }{\frac {p_{n+1}-p_{n}}{\log p_{n}}}=0}$

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

This result was originally reported in 2003 by Dan Goldston and Cem Yıldırım but was later retracted.[4][5] Then Janos 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.