mersenneforum.org lower bounds on incomplete factorizations
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 2008-06-14, 14:54 #1 J.F.     Jun 2008 23·32 Posts lower bounds on incomplete factorizations I am searching for all 'small' factors p < 2^55 of Mersenne numbers M(n) up to n=1e5. The Cunningham Project (in particular this site) is my primary source. However, I'd like to save myself the effort of trial dividing the remaining composite numbers, as that work probably has been done before. In the Mersenne database I see trial division bounds at 2^58 and sometimes more, for instance at n = 1061. That is exactly what I need. But what about the trial division performed on incompletely factored Mersenne numbers, like for instance M(1069)? Is there a way for people like me to see what range of trial division was attempted on such numbers?
2008-06-14, 16:23   #2
wblipp

"William"
May 2003
New Haven

22·32·5·13 Posts

Quote:
 Originally Posted by J.F. But what about the trial division performed on incompletely factored Mersenne numbers, like for instance M(1069)? Is there a way for people like me to see what range of trial division was attempted on such numbers?
Will Edgington tracks this in his lowm.txt file, although I suspect that many people don't report unsuccessful trial factoring. He reports that M(1069) has been trial factored through

37473613084215372416028665821312617743022228898297

Will Edgington's Mersenne Page is at
http://www.garlic.com/~wedgingt/mersenne.html

2008-06-14, 18:42   #3
R.D. Silverman

Nov 2003

26·113 Posts

Quote:
 Originally Posted by wblipp Will Edgington tracks this in his lowm.txt file, although I suspect that many people don't report unsuccessful trial factoring. He reports that M(1069) has been trial factored through 37473613084215372416028665821312617743022228898297 Will Edgington's Mersenne Page is at http://www.garlic.com/~wedgingt/mersenne.html
Preposterous. The number you give above is simply tha largest
factor of M1069 found via ECM. There is no guarantee that there
is not a smaller factor. Note that this number is 50 digits. The universe
isn't old enough to have done trial division through 50 digits.

 2008-06-14, 18:58 #4 J.F.     Jun 2008 23·32 Posts Thanks for the remarks. Will Edgington's data is definitely something I can put to use. I'd only wish the uncertainty could be removed. Code:  Note that some smaller trial factors may not have been attempted since my database updates presently assume that all factorers are trial factorers (see also the 'G' line below). (from http://www.garlic.com/~wedgingt/mersfmt.txt)

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