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Primes of the Form and Goldbach's `Other Other' Conjecture
Jon Grantham, Hester Graves
We compute all primes up to of the form . Calculations using this list verify, up to our bound, a less famous conjecture of Goldbach. We introduce `Gold…
An Elementary Proof of the Minimal Euclidean Function on the Gaussian Integers
Hester Graves
Every Euclidean domain has a minimal Euclidean function, . A companion paper \cite{Graves} introduced a formula to compute . It is the first formula for…
The Minimal Euclidean Function on the Gaussian Integers
Hester Graves
In 1949, Motzkin proved that every Euclidean domain has a minimal Euclidean function, . He showed that when , the minimal function is $ϕ_{\mathbb{Z}}(x) =…
Brazilian Primes Which Are Also Sophie Germain Primes
Jon Grantham, Hester Graves
We disprove a conjecture of Schott that no Brazilian primes are Sophie Germain primes. We enumerate all counterexamples up to .
The Minimal Euclidean Function on the Gaussian Integers
Hester Graves
The Minimal Euclidean Function on the Gaussian Integers
Euclidean Ideals in Quadratic Imaginary Fields
Hester Graves, Nick Ramsey
We classify all quadratic imaginary number fields that have a Euclidean ideal class. There are seven of them, they are of class number at most two, and in each case the unique clas…