## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Wednesday, January 29, 2014 — 4:00 PM EST

In 2013 Yitang Zhang proved that there are an infinitely many pairs of primes such that the two primes in each pair differ by no more than 70,000,000. One of the techniques he used to prove this is to reduce the problem down to three types of estimates, which he named Type I, Type II, and Type III. A refinement of his argument was given by the Polymath Project whose goal is to reduce the gap of 70,000,000 and did so to 4680. They obtained this number by strenghening Zhang’s estimates for Type I, Type II, and Type III. We examine these estimaes and show how these estimates imply Zhang’s theorem.

Location

MC - Mathematics & Computer Building

4062

200 University Avenue West

Waterloo, ON N2L 3G1

Canada

200 University Avenue West

Waterloo, ON N2L 3G1

Canada

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1