A couple of comments before too many people jump to too many conclusions. 1. Don't believe a word that E.T.Bell ever wrote. 2. I remember Selfridge commenting, as an example of Raphael Robinson's amazing competence, that his first program ran first time. R. On Wed, 20 Apr 2005, Schroeppel, Richard wrote:
I'm glad to see this on the web! Guy, is it practical to convert it to either an ascii file, or tex?
One notable omission is Speciner's work at MIT AI Lab c. 1970, using Schonhage-Strassen (now days we call this Karatsuba). He was beaten out by Gillies in finding M19937, showing that the faster machine sometimes beats a better algorithm.
I looked at Chris Caldwell's page on prime number records by date, mwntioned below. He supposes that Fermat probably knew that 223 | M29, since he knew the theorem about factors of Mp being 2kp+1, and that 47 | M23 and 233 | M37. I've come across some contradictory indications, but can't point to the source. It may be in some of Bell's biographical work, maybe The Last Problem. Another curiosity on Caldwell's page is a remark (by Robinson?) about his SWAC program that found M521,607,1279,2203, and 2281: It was Robinson's first program, and it worked the first time. This is hard to credit. Did SWAC provide builtin bugnums? The program must have been either in machine code or assembly language.
Rich
-----Original Message----- From: math-fun-bounces+rschroe=sandia.gov@mailman.xmission.com on behalf of Guy Haworth Sent: Wed 4/20/2005 4:00 AM To: math-fun@mailman.xmission.com Subject: [math-fun] 'Mersenne Numbers' snapshot of 1990
After an overlong delay following Richard Schroeppel's kind return-supply of a copy of my 'Mersenne Numbers' notes of 1983-1990, I have scanned them in to text-searchable pdf.
They are available at http://www.cs.reading.ac.uk/people/G.Haworth.htm?publications and specifically as http://www.cs.reading.ac.uk/common/publications/02116.pdf
This is the 22/01/90 version, and so a retrospective, looking back 15 years.
Please use as you see fit. If my scanning technique or technology proves to be significantly off the pace, I'll rescan.
I suppose it might be worth building a database, off which review-reports of this kind might be derived.
So I am interested in views of how to update the content, information management and presentation.
I'm also trying to find a copy of my 'Mersenne Numbers: Consolidated Results' which covered the collation of previous results, together with the ICL DAP's second-sourcing and occasional correction of those results.
Incidentally, Mersenne's conjecture about prime M(p) with p between 1 million and 2 million was disproved in 1996 with: M(1,257,787), the 34th prime M(p) and M(1,398,269), the 35th prime M(p)
I attended the Celebration of David Wheeler's work at Cambridge University's Computer Laboratory on Monday. There was brief mention of the Miller/Wheeler paper in Nature(1951) [v168, p868] which "ushered in the computer-age of prime-finding" . I see others agree ...
http://primes.utm.edu/notes/by_year.html#MW
The footnote is that their program was used to test the integrity of EDSAC 1.
Guy
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