# Belphegor's Prime and Harvey Dubner

For Halloween this year we released two videos about Belphegor’s Prime (on Numberphile).

If you’ve only seen part one, then part two is also well worth a look.

You may notice (in part one) that Tony Padilla makes mention of a “prime hunter” called Harvey Dubner.

Prior to publishing, I sent an email to Harvey because I wanted to include a picture of him in the video.

I received a reply… but unfortunately it arrived just after publication. The message came from Harvey’s son, Bob.

In a lovely email, Bob explained his father is now 90 years old.

He explained Harvey is in “pretty good” health, although suffering some memory problems and no longer does mathematics.

Bob, who was also instrumental in the prime number work, explained:

“I am, indeed, the designer of the “massive computer” we “built in the garage” – it actually was a series of software packages and special arithmetic hardware that I designed over the years between about 1981 and 2000. They mostly sat next to the couch in the family room; Dad liked to have the TV on when he did mathematical research.

It was around the year 2000, when FFT routines running on 400MHz and faster PCs overtook the hardware I had designed, that we gave up trying to improve my hardware. By the year 2005, I had incorporated the GMP software package and the magically tweaked routines written by George Woltman (of the GIMPS project) into our software. (I’m a pretty good programmer, but some of the people on the GMP project and Mr. Woltman are magicians. And my long-time engineering motto has been, “We steal only the finest.”)

We had a great run with the stuff I built; I believe that at our personal peak we had found about three-quarters of all the known prime numbers with more than 1,000 digits. But by the early 2000s, not only were general-purpose computers faster than my hardware (which ten years earlier had given us supercomputer capability) but also lots of people started using publicly available software to search for big primes, purely for bragging rights. So my father switched to looking for numbers he found interesting. Many packages are optimized around calculating the primality of number of the form k * 2^N. When k is one, you have the Mersenne primes, of course; but the calculations can run fast even for other values of k. But my hardware and software was general purpose, so he looked for numbers that were interesting in base 10 – for example, the palindromic primes, of which the Belphegor Primes are a subset. That was just for fun; he did a bunch of serious work in Sophie Germain Primes and Carmichael numbers. But it was always fun searching for big primes of various kinds.”

Bob included a picture of Harvey, adding:

“He remembers that he used to do a lot of math, but he can’t remember the math at all.

He likes being reminded about it, though, and so I happily send along this picture, which I shot about a year ago.

Coincidentally, a friend just today pointed me at https://youtu.be/zk_Q9y_LNzg, which is, I believe, the episode in question, so I am probably too late with the picture. But I figured I’d send it along anyway.

Thanks so much for your interest. If you decide to edit in my dad’s picture, please let me know. It would make him happy to see his image mentioned along with his work that way.”

So here’s the picture of Harvey - our thanks to him and to Bob.