"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.

Video of "An Unconditional Improvement to the Running Time of the Quadratic Frobenius Test"

A video of my talk on "An Unconditional Improvement to the Running Time of the Quadratic Frobenius Test" at the recent PAJAMAS conference is available on YouTube.

Since I am likely to have more talks available online in the future, I have created a talks page listing them all (at this moment, listing them both).

While I was at it, I created a papers page as well. My previous one had not been updated since 2014, and did not have great links. This one links to both the arXiv copies and the journals (for those which have been published).

"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.

Preprint of "An Unconditional Improvement to the Running Time of the Quadratic Frobenius Test"

A preprint of my paper is here. Keep me in your thoughts as I go through the submission/publication process.

Further results on "Grantham's Problem"

While it is gratifying to see a mathematics paper published, it is sometimes even more gratifying to see that paper cited, because it means that someone cares about the original publication.

A decade ago, I mentioned that someone had addressed a question I asked in a 2001 paper, which he called "Grantham's problem."

Now he and two authors have pushed the computations further, in the paper "Quadratic Frobenius pseudoprimes with respect to x² + 5x + 5".

The results put conditions on a pseudoprime with two prime factors. The known heuristics for the existence of pseudoprimes give ones with many prime factors, so it is not surprising, but it is good to see this evidence.

Talk on "An Unconditional Improvement to the Running Time of the Quadratic Frobenius Test"

I am about to give a talk on "An Unconditional Improvement to the Running Time of the Quadratic Frobenius Test" at the AMMCS conference.

Grantham's Problem

While reviewing the referee's 44 (sigh) suggested changes to my paper, I came across an article published last November entitled "Inefficacious Conditions of the Frobenius Primality Test and Grantham's Problem".

I have a problem named after me!

So the next time someone asks me, "What's your problem?" I can say, "Are there any composite numbers n ≡ ±2 (mod 5) such that x^(n+1) ≡ 5 (mod(n, x^2 + 5x + 5))?"

New Version of "There Are Infinitely Many Perrin Pseudoprimes"

I have reformatted There Are Infinitely Many Perrin Pseudoprimes (sometimes known as "There Are Infinitely Many Frobenius Pseudoprimes"). It now uses a more modern version of the TeX typesetting package. I also re-submitted it for publication after only 6 or 7 years. I think it holds up, though!

Corrected SERMON slides

I have posted a corrected version of my slides from SERMON.

SERMON 2005 Talk

I am giving a talk at the SERMON 2005 conference entitled, "Collecting primes with p²-1 827-smooth, or reduced sets for likely solutions to the $620 problem."

Here are the slides.