Pseudoprimes and Other Research

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2010-03-04T05:20:00.001-08:00

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Yet another new version of the paper

2010-02-20T14:57:00.000-08:00

I got the proofs back from the Journal of Number Theory, and they made a few minor changes (mostly capitalization and such). I'm having trouble ftp'ing to pseudoprime.com, so you can find the latest versions here on Google Docs.

Even newer version of paper!

2009-11-12T09:09:00.000-08:00

The referee had 9 additional suggestions after receiving my previous revision. I incorporated 8 of them, and the paper has now officially been accepted by the Journal of Number Theory. The latest version is here.

Elliptic Pseudoprimes

2009-10-22T10:09:00.000-07:00

Mathematics of Computation recently published an article by Siguna Müller entitled, "On the existence and non-existence of elliptic pseudoprimes". She refers to two of my papers (references [7] and [8]).

I have not looked much at elliptic pseudoprimes. In particular, in my 2001 paper, "Frobenius Pseudoprimes", I say,

This paper does not pretend to be an exhaustive treatment of all notions of pseudoprimality. For example, nothing is said about elliptic pseudoprimes [8].

Maybe I should look at them some more.

Newer version of paper!

2009-09-29T14:10:00.000-07:00

I have incorporated the referee's 44 suggestions and made other changes. The newest version of the paper is available here. The editor is sending it back to the referee. Hopefully this merry-go-round will stop soon!

Grantham's Problem

2009-09-02T09:00:00.000-07:00

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 Paper

2009-03-23T16:05:00.000-07:00

Well, this time I didn't take 6 or 7 years. After slightly more than two years, I've revised There Are Infinitely Many Perrin Pseudoprimes again. I used a more modern version of the journal's style guide, and I incorporated some comments an editor suggested. Now hopefully it'll go off to another editor (don't ask) and a referee!

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

2007-04-21T07:05:00.000-07:00

I am giving a talk at SERMON 2007 later today. Here are the slides.

Things Have Changed

2006-12-11T07:30:00.000-08:00

Since I last submitted that paper.

The journal that had been interested in publishing it no longer publishes things on that subject.
A paper can be turned down in 2 days.

Still, the "rejection" was very encouraging, saying

I would urge the author to submit his paper to a top-end number theory journal...

So I will, but I have to do some further (minor) reformatting.

New Version of "There Are Infinitely Many Perrin Pseudoprimes"

2006-11-28T14:32:00.000-08:00

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

2005-04-19T11:25:00.000-07:00

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

SERMON 2005 Talk

2005-04-14T13:24:00.000-07:00

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.

Welcome to the Blog

2005-04-14T13:23:00.000-07:00

I have create this new weblog to post updates on my mathematical research. It will not necessarily be updated frequently, but will contain links to talks, papers, and other items of interest.