Publication of "On the maximum gonality of a curve over a finite field"

My paper with Xander Faber and Everett Howe, "On the maximum gonality of a curve over a finite field" appeared in Algebra & Number Theory earlier this year. This is probably the fanciest journal my work has appeared in, though I owe most of the fanciness to my co-authors.

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.

Publication of "Finding a widely digitally delicate prime" in Integers

 

My paper "Finding a widely digitally delicate prime" appeared in the journal Integers earlier this year.

Publication of "On Integers Whose Sum Is the Reverse of Their Product" in Fibonacci Quarterly

 

My paper with Xander Faber, "On Integers Whose Sum Is the Reverse of Their Product" has appeared in the latest issue of Fibonacci Quarterly. It is my 13th published paper.

A freely-accessible version is available at the arXiv.

"Binary curves of small fixed genus and gonality with many rational points" appears in Journal of Algebra

 

My paper with Xander Faber, "Binary curves of small fixed genus and gonality with many rational points" appeared in the 1 May 2022 issue of the Journal of Algebra. This is my 12th publication (although its print publication precedes our ternary/quaternary paper, so I will have to renumber at some point).

"Proof of Two Conjectures of Andrica and Bagdasar" Appears in Integers

My paper, "Proof of Two Conjectures of Andrica and Bagdasar" has appeared in the journal Integers. It uses techniques from my earlier work to show that certain families of pseudoprimes are infinite. I hope that others find this technique useful.

"Ternary and Quaternary Curves of Small Fixed Genus and Gonality With Many Rational Points" Appears Online in Experimental Mathematics

 

My paper with Xander Faber, "Ternary and Quaternary Curves of Small Fixed Genus and Gonality With Many Rational Points," has appeared in Experimental Mathematics online. Based on my estimate of the journal's backlog, I expect print publication in 2023.

This is my tenth journal article published, although I may have to re-do the numbering in 2023.

"The abc Conjecture Implies That Only Finitely Many s-Cullen Numbers Are Repunits" Appears in the Journal of Integer Sequences

 

Catching up from earlier this year, my paper with Hester Graves, "The abc Conjecture Implies That Only Finitely Many s-Cullen Numbers Are Repunits" appeared in the Journal of Integer Sequences.

This is my ninth journal article published.

"Brazilian Primes Which Are Also Sophie Germain Primes" Appears in Integers

I am pleased that my paper with Hester Graves, "Brazilian Primes Which Are Also Sophie Germain Primes" has appeared in the journal Integers.

This marks my second publication this year, a feat I only equaled in 2014 (which was the last year I published anything). But the year is less than half over, and I have a lot of time to write stuff, so who knows whether I can make it to a third this year. (The length of the refereeing and editing process means probably no.)

This is only the fourth journal I've published in, after Mathematics of Computation, Journal of Number Theory, and the American Mathematical Monthly. I am hoping to expand that with my next few publications.

"An Unconditional Improvement to the Running Time of the Quadratic Frobenius Test" appears in Journal of Number Theory

I was just reviewing the entries on this blog and realized I had never posted that "An Unconditional Improvement to the Running Time of the Quadratic Frobenius Test" is appearing in the May 2020 issue of Journal of Number Theory. You can cite it as:

Grantham, Jon. An unconditional improvement to the running time of the quadratic Frobenius test. J. Number Theory 210 (2020), 476--480.

Publication of "Repeatedly Appending Any Digit to Generate Composite Numbers"

I'm proud to say that "Repeatedly Appending Any Digit to Generate Composite Numbers," a paper I co-authored with Witold Jarnicki, John Rickert and Stan Wagon, has appeared in the May 2014 American Mathematical Monthly. If you are an MAA member (which, um, I'm not), access it through their web site.

Print Publication of Constructing Carmichael numbers through improved subset-product algorithms

"Constructing Carmichael numbers through improved subset-product algorithms," co-authored with the late Red Alford, as well as Steven Hayman and Andrew Shallue, published online last summer, has been placed in the March 2014 issue of Mathematics of Computation.

That means if you want to cite it, you can now cite it as:
Constructing Carmichael numbers through improved subset-product algorithms. Math. Comp. 83 (2014), no. 286, 899-915.

I'm still waiting for it to appear in MathSciNet, so I can calculate my collaboration distance to various friends and acquaintances.