Since 2019, I've served as a mathematical advisor to the distributed computing project PrimeGrid, which searches for large prime numbers of various forms. Below you can find some information on the main PrimeGrid projects that I have been involved in.
In Spring 2025, I ran an undergraduate research project through the Illinois Mathematics Lab aimed at developing software to find the longest known arithmetic progression (AP) of prime numbers. The best existing algorithm was designed by Jarosław Wróblewski and optimized for searching for AP26's; since it has now found many AP26's and a few AP27's, our search is aimed at finding the first known AP28.
My IML students optimized Wróblewski's algorithm to target AP28's, improving its efficiency for that goal by roughly 8x. Subsequently, they developed several generalized versions of it that search for APs with common differences not accessible with the original algorithm; these result in additional speedups of 1.8x to 2.9x.
As of Fall 2025, we are continuing the project informally, with the goal of merging our algorithmic changes with Bryan Little's hardware optimizations and BOINC integration, to prepare it for future deployment on PrimeGrid. We are also working on using the Bateman-Horn conjecture to predict the expected number of APs that our programs will find, for the purpose of prioritizing which regions of the search space to explore first.
You can find the final report from the Spring 2025 IML project here.
I helped design PrimeGrid's Fermat Divisor Search (PPS-DIV), which ran from 2019 to 2021. Related links: