Colloquium
3:00 p.m., Tuesday (April 27th)
Math Annex 1100
Ben Green
PIMS & Mathematics Department, UBC
Arithmetic progressions of primes
The prime numbers 5,11,17,23,29 form an arithmetic progression
of length five, and a backofanenvelope calculation will confirm that
the 22 numbers 11410337850553 + 4609098694200k, k = 0,...,21, are also all
primes. Terry Tao and I have proved that in fact one can find arbitrarily
long arithmetic progressions of primes.
In the talk I will describe some famous open problems concerning primes,
and some famous open problems concerning arithmetic progressions, either
of which would imply this statement. Then I will try and explain how we
obtained our result without making the slightest dent in any of these
conjectures.
Refreshments will be served at 2:45 p.m.in the Faculty Lounge,
Math Annex (Room 1115).
