#
Gaps between primes

November 28 to December 2, 2005
at the

American Institute of Mathematics,
Palo Alto, California

organized by

Dan Goldston,
Sid Graham,
and Andrew Granville

## Original Announcement

This workshop will be devoted to the recent
work of Goldston, Pintz, and Yildirim on gaps between primes and
primes in tuples.
The work depends on a surprisingly effective variation of the Selberg
sieve, and it has connections and applications to other problems in
sieve methods.
We seek participants who are experts in sieve methods as well as
those who are not; in particular, we encourage those who may be unfamiliar
with sieves but have expertise in other areas of number theory to
attend.
The simplicity of the basic ideas should allow the participants to
quickly understand
both what is known and what are the main unresolved questions.
Further applications
and relationships to other areas of number theory will be explored.
The main topics for the workshop are:
- Approximations for primes in tuples and
their application to small gaps between primes
- Applications of the new approximations to sieve methods,
numbers with few prime factors,
and the parity problem
- Open problems such as bounded gaps between primes,
level of distribution of primes in arithmetic
progressions, the relationship between the Elliott-Halberstam
conjecture and the twin prime
conjecture, and further applications to other
problems.

## Material from the workshop

A list of participants.
The workshop schedule.

A report on the workshop activities.

Report of
working group activities.