PrimeGrid

Since 2019, I've served as a mathematical advisor to the distributed computing project PrimeGrid, which searches for large prime numbers of various forms.

Fermat Divisor Search

I helped design PrimeGrid's Fermat Divisor Search (PPS-DIV), which ran from 2019 to 2021.  This began with my investigation into which primes can, cannot, and are unusually likely to be divisors of Fermat numbers.  Related links:

• What primes can be Fermat divisors? (Or:  what's the deal with 19683?)
• Our finds:
  • 13 * 2^5523860 + 1 (1,662,849 digits, divides F_5523858, discovered by Scott Brown)
  • 27 * 2^7963247 + 1 (2,397,178 digits, divides F_7963245, discovered by Tom Greer)
• All known Fermat divisors (maintained by Wilfrid Keller)
• Primes of the form k * 2^n + 1 for k < 300 (maintained by Wilfrid Keller)

Miscellaneous links

• The 5000 largest known primes (maintained by Chris Caldwell)
• OpenPFGW (open-source software for primality and probable-primality testing)
• Web-based integer factorization calculator (by Dario Alpern)
• How to search for 26 primes in arithmetic progression? (by Jarosław Wróblewski)