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.

Publication of "Fibonacci primes, primes of the form 2^n-k and beyond"

 

Last year, my paper with Andrew Granville, "Fibonacci primes, primes of the form 2^n-k and beyond" appeared in the Journal of Number Theory.

Publication of "Ternary and quaternary curves of small fixed genus and gonality with many rational points" in Experimental Mathematics

I haven't kept up this blog in a couple of years, and I've had a few articles appear since then. Let's try to get caught up.

My paper with Xander Faber, "Ternary and quaternary curves of small fixed genus and gonality with many rational points" appeared in Experimental Mathematics in 2023.