digitized by Doug Anderson
|Corrections — Please Read
(4 December 1996)
|Mersenne was a Minim friar. Minims are not Jesuits. He was, however, educated by the Jesuits. Furthermore, Mersenne was not an Inquisitor. Indeed, he was probably quite a pleasant fellow. Please read these enlightening and scholarly emails that I received. (Learn the fate of his old residence!)|
Who was Marin Mersenne?
You are probably visiting here because of an interest in Mersenne Primes. It was not until the mid 20th century that Mersenne became known primarily for his Prime Number Conjecture. Historically, he was much better known for his correspondence with leading scientists of the day (hence the other Mersenne Mailing List). Interested in optics, he also been called (no pun intended) the Father of Acoustics. Here are some links that will tell you something about the man himself:
|a nice biography (and another picture!) courtesy of the Algebra Group WWW Server of the University of St. Andrews, Scotland. Here is a larger version of the same portrait (jpeg, 280×340, 9 KB). Thanks twice to Björn Hedin and to Björn Hedin|
|another nice biography by Richard S. Westfal of Indiana University, Bloomington as part of the wonderful Galileo Project at Rice University (my Mom’s school).|
|a biography from the Encylopedia Britannica Online. Evidently, Mersenne was the grandfather of the pendulum clock, or did he get the idea from Galileo?|
|a biography from the Encyclopedia Americana|
|a biography from the Grolier‘s Encyclopedia Windows CD-ROM|
|a book by Peter Dear, Mersenne And The Learning Of The Schools, is currently (4 July 1997) available at the Amazon dot Com cyberbookstore. I read Chapter 1: Introduction. And Chapter 2: Humanism and the Implications of Rhetoric. But I’m stalled near the end of Chapter 3: Dialectic, Probabilism, and “Mitigated Scepticism”. Lots of footnotes and a 21-page bibliography. US$40 plus US$4 shipping.|
Mersenne Numbers and Mersenne Primes
|MUST READ Chris Caldwell has an absolutely first-rate page Mersenne Primes: History, Theorems and Lists. He also maintains the definitive Largest Known Primes page.|
|Visit my Mersenne Number Library and Bibliography with a lot of articles and links to people like Hans Riesel (M3217), Landon Noll (M21701 and M23209), and Samuel Wagstaff (distribution of factors).|
|Here’s the link everybody is looking for: George Woltman’s Great Internet Mersenne Prime Search. People all over the world are using his program in an orchestrated search for the next Mersenne Prime. George has highly Pentium-optimized a specialized multiplication algorithm byRichard Crandall (of Perfectly Scientific, Inc — ‘the scientific algorithm company’, and formerly with NeXT) and Barry Fagin. 486, PowerMac, Alpha, HP users, almost everybody, can help, too. Dan Gilmore, of the San Jose Mercury News, wrote a newspaper article about GIMPS, dated June 22, 1996. Also Len Ruth and his students at The Sinclair Community College are searching.|
|(4 December 1996) GIMPS finds a new World’s Largest Prime Number! Joel Armengaud, running George Woltman’s program, found M1398269, the 35th known Mersenne prime. I’m hoping that Joel will send me a photo of himself taken on rue des Minimes in Paris.
|(1 September 1997) 22,976,221 – 1 is Prime! Another new discovery by GIMPS! The 36th known Mersenne prime is a whopper with 895,932 digits.
|(2 February 1998) Will they ever stop? 23,021,377 – 1 is Prime! Yet another new discovery by GIMPS! Not quite a million digits long, it is the 37th known Mersenne prime.
|(15 March 1997) George Woltman sends out periodic GIMPS newsletters. You can read them all on Will Edgington’s Mersenne Newsletters Page.|
|(9 February 1997) How fast is your PC? Lennart Grebelius now maintains an informative Mersenne Prime Benchmark page. The page should look familiar to GIMPS members. Can a Pentium 166 run faster than a Pentium 200? Lennart also tracks GIMPS progress in P90 CPU years/day. Great page!|
|(17 October 1996) By popular demand, Herb Savage has created some colorful, graphical representations of the current status of the Mersenne prime search. Check back periodically and watch gray turn to blue, blue to green, and maybe even a new, red pixel or two!|
|(31 January 1998) The Unofficial GIMPS Graphical Status Page by David J. Fred. Similar to Herb’s images, David graphically shows the current GIMPS staus to the highest p.|
|(15 March 1997) The February 1997 issue Wired Magazine has an item on George Woltman and GIMPS. See Wired News: Electric Word: Prime Time. Unfortunately, they misspelled Joel Armengaud’s name. Here is a scanned image of the original (250Kb).|
|The Mersenne Prime Mailing List. Communicate with people discussing anything and everything about Mersenne Primes. You don’t have to write anything, you are welcome to just listen in. You can read all of the old posts in the list’s archives.|
|John Vinopal has been working on a helpful Mersenne Primes page. He explains some things quite well.|
|His Mathematica notebook on Mersenne Primes has been made available by Paul Wellin. He also has one on searching for perfect numbers. You don’t have Mathematica? To view his notebooks, get a free copy of MathReader.|
|Susan Stepney discusses Mersenne primes, the Lucas-Lehmer test, Perfect numbers and more.|
|A post dated 2 Apr 1992 by David Slowinski to comp.sys.super, comp.unix.cray, and sci.math (with a follow-up by Bob Silverman). He mentions different machines in the hunt and that M756839 took 19 hours on a Cray-2. Here is Bob Silverman’s reaction to the discovery of M756839.|
|Courtesy of Eric’s Treasure Trove of Mathematics, a page that lists “Mersenne numbers” and their factorizations. This page defines a Mersenne number to be 2^n-1 (n not necessarily prime).|
|This is the FORTRAN program (PrimeZilla) that found M110503 on the NEC SX-2 at the Houston Advanced Research Center (HARC). Optimized for the idiosyncrasies of parallel and vectorized computing, it ran at about 2 gigaflops and took about 11 minutes to test M110503.|
|David Slowinski’s announcement of his and Paul Gage’s discovery that M859433 is prime. Thanks to Warut Roonguthai for the link.|
|There is a growing list of Mersenne freeware. You should be able to find something that will run on your computer. The page is now maintained by and hosted by Conrad Curry. And a big Thanks! to Michael Taylor who was the previous host and maintainer.|
|Some of us Mersenne guys had a meeting at the Tied House and I took some photos. They turned out pretty well.|
|(1 October 1996) David Slowinski and Paul Gage struck paydirt once again! They found M1257787, the 34th known Mersenne prime. Here’s where you can read all about it:
|(1 Oktober 1996) Von Die Zeit “Auf Primzahl-Jagd im Internet”. Vielen Dank!, Cornelius Caesar.|
|(10 October 1996) Jeffrey O. Shallit has a wonderful Mersenne Bibliography with many entries that I was not aware of.|
|(29 October 1996) GIMPS’s George Woltman was on Canadian radio. George did a great job, as did the program’s host. I decided that the event warranted its own wwweb page.|
|(4 December 1996) This is wonderful! The GIMPS project is exciting some young imaginations. More and more young people are becoming interested in Mersenne primes. The Student’s Mersenne Prime Page has just gone online. Oliver Grebelius is a 7th grade student in Sweden. Let’s wish him great success.|
|(8 December 1996) I am awarding the Most Beautiful Prime Page Prize to Marlene Menard. You’ve seen how professional mathematicians design Mersenne wwweb pages. Take a look at how a professional graphics artist views the Great Internet Mersenne Prime Search.|
|(16 January 1997) Herr Factormeister Will Edgington has somehow found time to do a page on Mersenne numbers. This page is recommended reading.|
|(26 March 1997) From the 1982 Guinness Book of World Records, Harry Nelson and David Slowinski “celebrate their discovery, clothed in computer printouts.”|
|(22 April 1997) Psssssst! Yeah, you. Come over here. Do you want to see a picture of BESK? This baby can crank out nearly three thousand 40-bit multiplies per second. Learn more from Hans Riesel himself, plus some stories about his search for M3217.|
|(4 July 1997) Largest Known Prime Number Discovered on the Vietnamese Association for Computing, Engineering Technology, and Science (VACETS) site. Dated 10 Sept 96, it apparently has been hiding from the search engines — I only recently found it. Very well written, I recommend this page even though my name is misspelled.|
|(4 July 1997) Bekannte Mersenne-Primzahlen von Argee. Kriterium von Lucas-Lehmer, Kriterium von Euler, Perfekte (vollkommene) Zahlen, und Literaturnachweis.|
|(4 July 1997) I don’t know why I didn’t link to this before. Robert Zubek has created a number of clean-looking GIMPS graphics, buttons, banners, etc. Check them out!|
|(31 January 1998) For every Mersenne Prime there is a corresponding Perfect Number. Naohiro Nomoto is a mathematics fan in Japan. He has made a Perfect Number Home Page. Also available in Japanese.|
Mersenne Odds and Mersenne Ends
|Here’s an article on acoustics that discusses Mersenne’s Laws from the Encylopedia Britannica Online|
|The Wave Theory of Sound by Allan D. Pierce mentions some of Mersenne’s contributions to acoustics. Courtesy of the Acoustical Society of America.|
|Mersenne reproduced some experiments of Marin Getaldic. Which experiments? Visit this devil in mathematics whose inventions were feared by his compatriots and even more by his enemies. (Croatian site, .hr = Hrvatska).|
|Pop Quiz: What is a Mersenne telescope? Give an example of a modern application. (NASA site.) Thanks go to Brian Jones. BTW, Stevick-Paul telescopes are similar to Mersenne telescopes.|
|Coming Attraction: Magnetic Monster! Starring the SWAC as MANIAC with music by Mersenne and sets by Alex Hurwitz. Can the Earth be saved? I have it and hope to make a Quicktime clip. Here is a sneak preview (and a mirror). Und hier ist der Inhalt.|
|A series of five articles on Doctor Robert Fludd (1574-1637) By Sharon M.W. “A French scientist and author named Marin Mersenne accused Fludd of being a magician, an atheist and heretic.” Articles 1, 2, 3, 4 and 5. Mersenne is mentioned in Articles 4 and 5.|
|Bagpipes? Mersenne and bagpipes? What? (Go there and use your web browser’s Search function.)|
|If you are a young programmer or mathematician and you’ve never heard of him, do yourself a favor and visit the World’s Best Programmer. And here is the proof.|
|Everybody know what twin primes are, but how many of you have ever seen prime twins? Walt Colquitt is going to retaliate against me for this, but it’s worth it.|
|Bah! Who cares about World Record Mersenne Primes? Here is a page about what matters the Most about Mersenne primes!|
|There are photographs of Mersenius a crater and a rift on the moon named in honor of Mersenne (US Navy site). The photos are also on a French site Navigation sur la LUNE. Susan Stepney kindly designed a Mersenne on the Moon page to help you locate the crater on the moon’s surface — in astronomical terms, it’s in the lower left-hand corner. Thanks to Richard Easther for tracking down Mersenius for me.|
|(22 July 1997) Mersenne was a Minim priest and lived in the Minim convent in Paris. It was destroyed during the French Revolution. But there is still a street named rue des Minimes. You might be surprised.|
Hopefully this will answer some questions. I’d like to add a few more like “Fermat”, “Euler”, “Uhler”, “Lehmer”, “Knuth”, “Kraitchik”, and especially “Fauquembergue”, etc. Any volunteers?
|(3 August 1996) The name of Marin Mersenne. The correct pronunciation of Marin was a surprise to me.
20 Kb audio file in WAV format. Recorded and spoken by Timour Jgenti, et ici en Français
|(3 August 1996) The name of François Édouard Anatole Lucas. The s in Lucas is silent.
30 Kb audio file in WAV format. Recorded and spoken by Timour Jgenti, et ici en Français
|(3 August 1996) The name of Anatolii Alekseevich Karatsuba.
27 Kb audio file in WAV format. Recorded and spoken by Timour Jgenti, et ici en Français
|(6 August 1996) The name of Emma Markovna Trotskaia (Emma Lehmer).
22 Kb audio file in WAV format. Spoken by Olga Sorkin.
|(6 August 1996) The name of Ivan Mikheevich Pervushin.
21 Kb audio file in WAV format. Spoken by Yuri Sorkin.
|(14 October 1996) The name of Hans Riesel.
21 Kb audio file in WAV format. Recorded and spoken by Oliver Grebelius.
|Links? You want links? Keith’ll give you links! Keith Matthews maintains the Number Theory Web with sites in North America and Australia.|
|Mersenne People. Stand up and be counted! Add your name to the list of those who have an interest in Mersenne primes.|
Stuff To Do
|Hang a photo or two of Walt and the NEC SX-2.|
|Solicit other old Mersenne Number hunters for old photos, source code, horror stories, etc.|
|Add more Stuff To Do.|