Jon Grantham

collaborators

3 papers

math.NT2026

On a remark of Serre

Katie Ahrens, Jon Grantham

Inspired by a remark of Serre, we extend the search for primes $p$ such that the maximum Hasse bound for the number of points on an elliptic curve over $F_{p^{5}}$ is not ac…

math.NT2025

Primes of the Form $m^{2} + 1$ and Goldbach's `Other Other' Conjecture

Jon Grantham, Hester Graves

We compute all primes up to $6.25 \times 1 0^{28}$ of the form $m^{2} + 1$ . Calculations using this list verify, up to our bound, a less famous conjecture of Goldbach. We introduce `Gold…

math.NT2025

No new Goormaghtigh primes up to $1 0^{700}$

Jon Grantham

The Goormaghtigh conjecture states that the only two numbers which have two non-trivial representations as repunits are $31$ and $8191$ . We call such a prime number a {\it Goormagh…

On a remark of Serre

Primes of the Form m2+1 and Goldbach's `Other Other' Conjecture

No new Goormaghtigh primes up to 10700

Primes of the Form $m^{2} + 1$ and Goldbach's `Other Other' Conjecture

No new Goormaghtigh primes up to $1 0^{700}$