...continued In Raphael M. Robinson,"Mersenne and Fermat numbers," Proc. Amer. math. Soc., 5 (1954) 842-846. (Announces the discovery of the 13th through 17th Mersenne primes --the first Mersenne primes found by electronic computer), Robinson credits Turing (presumably on "Baby" - the Manchester Mark 1) as being the first to test Mersennes! > In 1951, the first application of an electronic computer to testing > Mersenne numbers for primeness was made by A. M. Turing at the > University of Manchester; however, no new primes were found, and no > remainders were saved for purposes of comparison. > In 1952, a program for testing Mersenne numbers for primeness on > the SWAC (the National Bureau of Standards' Western Automatic > Computer, at the Institute for Numerical Analysis in Los Angeles), > planned and coded by the author, using Lucas's test, was carried > out, with the cooperation of D. H. Lehmer and the staff of the > I. N. A. My thanks are due especially to Emma Lehmer, who did > various auxiliary computations, including checking some of the > results obtained against earlier results. The program was first > tried on the SWAC on January 30, and two new primes were found that > day; three other primes were found on June 25, October 7, and > October 9. > > At that time, the total memory of the SWAC consisted of 256 > words of 36 binary digits each, exclusive of the sign. For the > Mersenne test, half of this memory was reserved for commands. Since > successive squarings of numbers less than the modulus 2n-1 are required, > this modulus was restricted to 64 words, so that the condition > n < 64 * 36 = 2304 was imposed. The estimated running time for the > program was 0.25n3+125n2 microseconds, and the actual time was in fair > agreement with this. Thus, roughly speaking, the testing time was a > minute for the first and an hour for the last of the five new primes. > Each minute of machine time is equivalent to more than a year's work > for a person using a desk calculator. The full text is hosted by Luke Welsh at http://www.scruznet.com/~luke/lit/lit_024s.htm (That has O(n^3), more than George's great implementation of the LL test. The Lucas-Lehmer algorithm was created in 1930, but they must have used Grammar School multiplication as the Karatsuba method or Fourier Transforms had not been invented yet). Ribenboim in The New Book of Prime Number Records also states that the first was Turing in 1951 (I believe incorrectly). Turing's designs (1945-46) for the Pilot ACE, which was finally built in 1950 at the National Physics Laboratory after Turing's resignation, were not incorporated directly into "Baby" - the Manchester Mark 1. The NPL is in Teddington, south of London. Turing started work in Manchester in March 1948, by which time "Baby" was nearly completed. It was completed on June 21st 1948. The computer that Turing was working on from June 1948 onwards was the "Baby", not his Pilot ACE. But, Chris Caldwell's excellent Prime Pages at http://www.utm.edu/research/primes/notes/by_year.html#MW > It is interesting to note that in 1949 the topologist M. H. A Newman > used the prototype Manchester electronic computer (with 1024 bits of > storage) to make the first attempt to find Mersenne primes by computer. > Perhaps because Alan Turing worked on this machine from 1948 to 1950, > and improved the program by Newman, this first attempt at finding > primes by (electronic) computers is sometimes attributed to him (e.g., > [Robinson54] and [Ribenboim95, p93]). The excellent Alan Turing > Internet Scrapbook has a picture of this machine. The Scrapbook has links to pictures of the Pilot ACE and "Baby". The Cambridge University EDSAC, based on EDVAC, was operational on May 6th 1949 (not 1948 as erroneously reported in some sources), but still before EDVAC, which wasn't working until late 1951. So before SWAC or EDVAC there were already 3 working electronic stored programme computers, which although slower had a couple of superior concepts. The ERA Atlas I (or, 1101 in its commercial designation) which was delivered to the Navy in December 1950 had a drum memory of 16,384 24-bit words, but no stored programme. http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Newman.html says of Professor Newman:- > In 1942 he joined the Government Code and Cipher School and worked > there with Turing. At the end of the War he was appointed to a chair > at Manchester and, 3 years later, he appointed Turing to the post of > Reader in Mathematics at Manchester. Andrew Hodges in the Alan Turing Internet Scrapbook writes:- > In February 1946, as you can read more about in my book, Newman wrote > to von Neumann that he was > hoping to embark on a computing machine section here, having > got very interested in electronic devices of this kind during > the last two or three years. By about 18 months ago [i.e. soon > after D-Day, and a year before von Neumann's EDVAC report] I > had decided to try my hand at starting up a machine unit when > I got out. It was indeed one of my reasons for coming to > Manchester that the set-up here is favourable in several > ways... I am of course in close touch with Turing... > Note that at this date, Turing had not even had his ACE proposal > accepted by the National Physical Laboratory; these were very early > days. > > Newman's intention was that the machine would be used for pure > mathematical work in algebra and topology, for instance the Four > Colour Theorem. The Royal Society approved the project and allocated > a grant to Newman for salaries and construction totally £35,000 > (about a million pounds in real terms now), with the comment that > 'Newman himself, because of his mathematical background and wartime > experience, is particularly well qualified for directing this project.' > At that stage, early 1946, Newman expected that that the American > Iconoscope would become available as the storage system. But it didn't > work. Meanwhile at the radar establishment, TRE, the top electronic > engineers had found themselves suddenly out of a job in August 1945. > F. C. Williams looked around for a leading-edge project. He soon > heard that the possibility of building electronic computers was in > the air and that creating a storage system was the main technological > bottle-neck. continued... Paul Landon _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
