The finding of the 32nd Mersenne

By Chris Caldwell

Adrian Powell recalls the discovery of the 32nd Mersenne

It was roughly 7 pm on Wednesday 19th February 1992, when a Cray Research Analyst at Harwell Lab in Didcot, Oxfordshire, UK was just about to start a regular software maintenance slot on the research Labs Cray-2 supercomputer.

It had been a busy few days with one thing and another in preparation to test the very latest and greatest Unicos operating system, which was released to the field on a regular basis.  Over the last couple of days the analyst had been busy building and configuring this latest software release, leaving little time for the kind of system checks that need to be carried out on a weekly basis.

On the Monday of that week though, he had briefly displayed a logfile which was being produced by a special program called mprime.  mprime had been installed onto the machine a few weeks back by the analyst, and consisted of a program which ran when the system was completely idle which had been written to find very large prime numbers called Mersenne primes.  In the course of finding these numbers, the program also ran cross checks which high lighted any potential problems with the machine. Something which needed to be detected and isolated very quickly when dealing with a machine whose primary job was run computer programs used for simulations and analysis in the nuclear industry.

Mersenne primes numbers were not only very long, but notoriously difficult to find. The program mprime had been written by a well respected computer scientist at Cray Research Inc in the USA called David Slowinski. Working with another computer scientist called Paul Gage, David ran an unofficial project in house at Cray to find large and large Mersenne Prime numbers, making use of small amounts of idle time on Cray supercomputers housed within the company, again with the upshot of being used to ensure that systems performed flawlessly.

Some years earlier, the site analyst at Harwell lab remembered seeing a large red poster hung on a wall of a UK Cray Research facility.  The poster contained an almost never ending number of digits, entitled the 29th Mersenne prime.  Although the analyst was familiar with large prime numbers and had spent time in the past producing fast computer programs in order to find large prime numbers, this relatively huge number looked absolutely incredible.  Thus the analyst decided to contact the author of the program, David Slowinski in order to see if the program could run on the Cray-2 Supercomputer housed at Harwell.

David Slowinski showing his usual enthusiasm for such things, happily obliged by providing the analyst with the program.  The analyst spent the next week modifying the way in which the program was run in his spare time, eventually coming up with the finished article. In late January 1992, the program was set to work; starting up when the system was completely idle, then going into hibernation when users started up programs on the machine.

On Monday 17th February, the analyst had noticed a strange entry in the mprime logfile.  Before he could investigate further the phone rang.  Immediately changing his attention to the nature of the call, the analyst completely forgot about the logfile entry; that was until just before the start of his software test slot on Wednesday.  In a brief period just before the beginning of his test slot, the analyst decided to take another look at the logfile.  The logfile contained reams and reams of entries, but near the end an entry '756839 prime' stood out. Surely it couldn't have been that easy to find a Mersenne prime the analyst thought.  The previous Mersenne Prime number had been found back in 1985.  This must be some kind of malfunction of the software or spoof entry.  The analyst called into his office a couple of customer staff who were due to work with him that evening.  As they peered at the screen, they appeared less skeptical about the find, and prompted the analyst to make a call to whomever had supplied the program.  Cautiously the analyst rang David Slowinski at Cray in the USA, and told him about the entry.  The entry actually referred to 2 to the power 756839 being a prime number, something that was impossible to prove unless the Mersenne proving theorem was used.  To the analyst's surprise David Slowinski actually responded with a "well done", and that he would get back after the number had been verified.

David Slowinski proceeded to use Cray's latest and greatest machine to verify the find; the brand new Cray C90 super computer, housed at Chippewa Falls in Cray's Wisconsin facility.  It took 19 hours of cpu time for the Cray-2 supercomputer to test 2⁷⁵⁶⁸³⁹-1, but the same test ran in only just over 3 hours of the new 16 cpu Cray C90.  Slowinski must have practically dedicated the C90 to the task as later on that evening, the analyst received an email to the effect that the number had indeed been verified on the C90. In the days that followed the new find was also verified by Richard Crandall, Chief Scientist at NEXT computer, as it was important to retest using a different computer architecture and software.

On March 25th 1992, the new discovery was announced to the world by both Cray and Harwell Lab, and large amounts of press coverage followed; some good and some bad.  The biggest problem was that although finding the new prime appeared to be a momentous, if not incomprehensible task, the fact that the number could not actually be used for anything, being just too big seemed to annoy many people.  The press often forgot to mention that the program provided a critical role in ensuring machine integrity.  The press coverable culminated in the UK TV show 'Tomorrows World' giving a slot to the find, where a presenter was seen running through a huge printout which was provided by the Cray analyst who discovered the number.

The discovery was actually officially credited to Harwell Lab, as they owned the Cray-2 on which the number had been found.  A little later that year David Slowinski actually visited the Harwell Site, which was seen as a good publicity exercise.  Internally within Cray special badges were produced to commemorate the find, and Harwell commissioned their official photographer to take pictures of the site people who were involved.

I do have photo's and press cuttings of the occasion, but I'm not sure that we can make the public on an internet site as I have lost contact with other people in the pictures.  I've also just found the video from Tomorrows World TV show!

Written by Adrian Powell, February 2006.