Publication of "No New Goormaghtigh Primes up to 10^700"

 

My paper, "No New Goormaghtigh Primes up to 10⁷⁰⁰" appeared in Integers last year.

This was a super-fun paper to write. I had not heard of the Goormaghtigh Conjecture until a virtual talk I attended during the pandemic. I stopped listening 10 minute in when the speaker moved on to generalizations and had a hard time stopping thinking about the topic.

The conjecture is that the only two numbers which are repunits (all 1s) in two different bases are 31 and 8191. I came up with the idea of restricting to prime solutions and was able to show that those are the only two such numbers up to 10⁷⁰⁰.