Department of Mathematics

Generalized Arithmetic Progression (GAP) Page

Welcome to the GAP Page!

The four of us (Jeff Vanasse, Michael Guenette, Marcus Jaiclin, and Julian Fleron) have been working to find various examples of Generalized Arithmetic Progressions of primes. This page exists to show the most up-to-date list of examples of GAPs, as well as references and information about GAPs.

So, what is a GAP, and how did we come to start looking for them? Our work started with a paper by Andrew Granville in the MAA (Mathematical Association of America) journal The American Mathematical Monthly, entitled "Prime Number Patterns". In it, Prof. Granville considered many consequences of the recent paper of Ben Green and Terry Tao, in which they showed that there are infinitely many k-term arithmetic progressions of primes. (See refereneces below.) Prof. Granville also said, "We have been unable to find a 3-by-3-by-3 GAP of distinct primes." This was a challenge to us and started the mathematical journey described here.


Computing Tools

This project would not have been possible without open source computing projects, for which we are grateful: