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Old 2015-06-17, 19:00   #1
fivemack
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Default 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(18717503768422534169234360964298858644141980040724787645377043601378871808778579200436674144778412771881449536099188734805437946727135080401726899693544912723158282644268263809549050312074756009395032732734096413998083144808972811916874168409343263457320974860787262675643677709702391580114506527801,2^991-1)^2)

Last fiddled with by fivemack on 2015-06-17 at 19:28
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Old 2015-06-17, 19:15   #2
fivemack
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Default 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 century-old mathematical table

CAMBRIDGE, UK, 22 JUNE The last gap in a table published in 1925, of factorisations of the so-called Mersenne numbers (2^n-1 where n is a prime), was filled in on 17 June this year, as Tom Womack, a Cambridge amateur mathematician, completed a two-month calculation on a high-end desktop computer, using software developed by Jason Papadopoulos to combine the results of quadrillions of calculations (equivalent to nine years on that high-end desktop computer) performed by a world-wide 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^n-1; 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^n-1 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 - 2^991-1 - 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? 2^991-1=

8218291649 x 41473350001 x 231620367206687 x
6721885469050382920298612421830968178768028093133627640714502537112053019071272802490029644416444090606146146238871876925423959
x 39437300765327204031983243120992095727633141975484859958380479021870710828340701521806772849536517037509868664540317823526815309243487991

Last fiddled with by fivemack on 2015-06-17 at 20:57
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Old 2015-06-17, 19:40   #3
R. Gerbicz
 
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Code:
lift(Mod(204586912993508866875824356051724947013540127877691549342705710506008362275292159680204380770369009821930417757972504438076078534117837065833032974336,2^991-1)^2)
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Old 2015-06-17, 21:10   #4
R.D. Silverman
 
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Quote:
Originally Posted by fivemack View Post
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 century-old mathematical table

CAMBRIDGE, UK, 22 JUNE The last gap in a table published in 1925, of factorisations of the so-called Mersenne numbers (2^n-1 where n is a prime), was filled in on 17 June this year, as Tom Womack, a Cambridge amateur mathematician, completed a two-month calculation on a high-end desktop computer, using software developed by Jason Papadopoulos to combine the results of quadrillions of calculations (equivalent to nine years on that high-end desktop computer) performed by a world-wide 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^n-1; 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^n-1 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
This last attribution is only partially correct. Coppersmith had suggested it previously and years before I had informally suggested
[in this forum] that one could save sieving by doing more than one number at once.
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Old 2015-06-18, 15:32   #5
R.D. Silverman
 
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Quote:
Originally Posted by fivemack View Post
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 century-old mathematical table

CAMBRIDGE, UK, 22 JUNE The last gap in a table published in 1925, of factorisations of the so-called Mersenne numbers (2^n-1 where n is a prime), was filled in on 17 June this year,
This is not quite true. The ORIGINAL tables only went up to n = 600. These base 2 tables, as well as the rest of the original book
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 2015-06-18 at 15:32
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Old 2015-06-26, 15:19   #6
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Now that M991 is completed, the smallest Mersenne number which has not been fully factored is M1213.
(Followed by 1217, 1229, 1231, 1237, 1249, 1259 and 1277, which together are the only such exponents below the Mersenne prime M1279.)
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Old 2015-06-26, 17:54   #7
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Quote:
Originally Posted by Qubit View Post
Now that M991 is completed, the smallest Mersenne number which has not been fully factored is M1213.
There is a 63 digit cofactor missing on mersenne.ca see http://factordb.com/index.php?query=M%281213%29. The remaining cofactor is a C297.
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Old 2015-07-04, 18:26   #8
pinhodecarlos
 
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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
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Old 2015-07-04, 19:16   #9
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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.
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Old 2015-07-04, 20:12   #10
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Forgot to refresh the pages. I wasn't seeing the new links. Thank you.
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