20150617, 19:00  #1 
(loop (#_fork))
Feb 2006
Cambridge, England
18EE_{16} Posts 
M991 press release?
The factorisation of M991 has completed (p127 * p137). 1539 hours on six cores i7/4930K for the 48.3M^2 matrix.
I'm wondering whether it's worth at least trying to put out a press release  this is the last entry left in a table with a history going back to 1925 of numbers with a history going back to 1644, there's the nice sportsmanship angle if we mention that the Bonn group left this one for the amateurs, 'plucky amateurs with computers in sheds' isn't too bad for the upcoming silly season. I have informed Sam Wagstaff. Code:
lift(Mod(18717503768422534169234360964298858644141980040724787645377043601378871808778579200436674144778412771881449536099188734805437946727135080401726899693544912723158282644268263809549050312074756009395032732734096413998083144808972811916874168409343263457320974860787262675643677709702391580114506527801,2^9911)^2) Last fiddled with by fivemack on 20150617 at 19:28 
20150617, 19:15  #2 
(loop (#_fork))
Feb 2006
Cambridge, England
14356_{8} Posts 
Draft devoid of merit
Here's a draft; I'm sure there are people here who have written press releases for a living, and I'd like them to have a go at hammering it into shape.
 Internet amateurs complete centuryold mathematical table CAMBRIDGE, UK, 22 JUNE The last gap in a table published in 1925, of factorisations of the socalled Mersenne numbers (2^n1 where n is a prime), was filled in on 17 June this year, as Tom Womack, a Cambridge amateur mathematician, completed a twomonth calculation on a highend desktop computer, using software developed by Jason Papadopoulos to combine the results of quadrillions of calculations (equivalent to nine years on that highend desktop computer) performed by a worldwide team using other software developed by Thorsten Kleinjung of the Ecole Polytechnique Federale de Lausanne in Switzerland. Allan Joseph Champneys Cunningham published in 1925 the results of his lifetime's work on the factorisation of numbers of the form a^n1; these Cunningham Tables have been the impetus for a great deal of work by many mathematicians, speeding up with the invention of the computer. Their main contribution to number theory has been the development of the number field sieve algorithm, which can be used for any number but for which these Cunningham numbers are especially suited. Sam Wagstaff at Purdue University in Indiana took over the tables in 1983 and has coordinated most of the subsequent work. In 2008 Joppe Bos used a room full of 215 PS3 consoles to look for small factors of 2^n1 for n between 1000 and 1200, and found seven over about twelve months. In 2013 Arjen Lenstra of EPFL devised a new technique which allowed factorising many Mersenne numbers simultaneously; over the next year and a half he and his team used it to fill in all but one of the gaps in the table. One number remained  2^9911  which the team at the Internet forum www.mersenneforum.org, who had earlier knocked off 821, 853, 859, 877 and 941, dealt with over the first half of 2015. The answer? 2^9911= 8218291649 x 41473350001 x 231620367206687 x 6721885469050382920298612421830968178768028093133627640714502537112053019071272802490029644416444090606146146238871876925423959 x 39437300765327204031983243120992095727633141975484859958380479021870710828340701521806772849536517037509868664540317823526815309243487991 Last fiddled with by fivemack on 20150617 at 20:57 
20150617, 19:40  #3 
"Robert Gerbicz"
Oct 2005
Hungary
10110100010_{2} Posts 
Code:
lift(Mod(204586912993508866875824356051724947013540127877691549342705710506008362275292159680204380770369009821930417757972504438076078534117837065833032974336,2^9911)^2) 
20150617, 21:10  #4  
Nov 2003
16444_{8} Posts 
Quote:
[in this forum] that one could save sieving by doing more than one number at once. 

20150618, 15:32  #5  
Nov 2003
2^{2}·5·373 Posts 
Quote:
were finished quite a while ago. The extension to n=1200 was done later by Dick Lehmer and John Selfridge. [I do not know the exact date; it was before 1970] Last fiddled with by R.D. Silverman on 20150618 at 15:32 

20150626, 17:54  #7  
Apr 2013
Germany
3·103 Posts 
Quote:


20150704, 18:26  #8 
"Carlos Pinho"
Oct 2011
Milton Keynes, UK
5×7×139 Posts 
Tom,
2,991 is still in Sam's most wanted page and not in the latest results page http://homes.cerias.purdue.edu/~ssw/cun/page130. http://homes.cerias.purdue.edu/~ssw/cun/want129 Carlos 
20150704, 19:16  #9 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{4}·11·53 Posts 
It is on page 131 (as well as three more numbers).
There is also the usual page summary letter for page 130 and the associated updated wanted list. 
20150704, 20:12  #10 
"Carlos Pinho"
Oct 2011
Milton Keynes, UK
5×7×139 Posts 
Forgot to refresh the pages. I wasn't seeing the new links. Thank you.

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