Thursday, March 08, 2018

Another Conjecture of Goldbach

Here are the slides for a talk I am giving this weekend at the SERMON conference in Johnson City, TN. The basic question addressed is as follows.

Look at all numbers a such that a2+1 is prime. (The sequence starts 1, 2, 4, 6, 10... ) Goldbach conjectured that any number (other than 1) in that sequence is the sum of two previous numbers.  So 2=1+1, 4=2+2, 6=2+4, 10=4+6, etc. We verify this for a up to 2*1014 and explore how easy it is to find these sums. This is joint work with Hester Graves.

Saturday, October 29, 2016

Parallel Computation of Primes of the Form x2+1

Today I gave a talk on Parallel Computation of Primes of the Form x2+1 at Towson University, at the first MASON conference.
You can see my slides here.

I computed all such primes up to 6.25x1028.

Tuesday, May 13, 2014

All My Reprints

Inspired by the availability of a reprint for my latest publication, I have updated my list of reprints. So 2 papers this year, but 6 in total over the past 20 years! I have two projects in the computations-in-progress-but-not-yet-written-up stage, so hopefully I'll end up somewhere between the two over the next few years.

Full Text of "Repeatedly Appending Any Digit to Generate Composite Numbers"

The American Mathematical Monthly recently e-mailed my co-authors and me a PDF copy of our article. The e-mail contained the line, "You may post it on and your personal website if you so choose." Very reasonable!

It is available at

So you can read it even if you don't otherwise have access to the Monthly, which Wikipedia tells me is the "most widely read mathematics journal in the world."

Friday, April 18, 2014

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.

Wednesday, December 18, 2013

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.

Monday, November 04, 2013

Towards an Erdős–Bacon number of seven

Erdos head budapest fall 1992Kevin Bacon (cropped) When I noted earlier this year that I was on my way to having an Erdős number of 3, due to either of two upcoming papers, a friend asked if I had an Erdős–Bacon number. My lack of a film career prompted me to answer, "no". I once appeared as an extra in a scene filmed for Lucid Days in Hell, but that scene was cut from the movie. So I didn't see how that helped.

But recently while reading a biography of Jim Henson, another thought came to me: what if I could use TV shows? Henson appeared on a TV show called Afternoon, hosted by Willard Scott and Mac McGarry. I appeared on It's Academic, hosted by Mac McGarry. That's two degrees of separation from Jim Henson! And Willard Scott! But what about Kevin Bacon?

Well, Henson appeared in The Muppet Movie with Austin Pendleton, who appeared in Starting Over with Kevin Bacon. Boom, if you allow TV shows (and you probably shouldn't), I have a Bacon number of four, and an Erdős–Bacon number of seven.