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Old 2011-12-16, 18:48   #1
Stargate38
 
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Default C166 from 10^455-1?

Why didn't anyone factor the cofactor of (10455-1)/(1091-1) yet? It's well within the range of GNFS or SNFS.

Here's the decimal expansion (166 digits):

Code:
4550956748305222152126018815762238940620303956367340855900091266114182783163428849423951840315664063783883817473128035867761145293485421290359307345105428632108260961
This number has been left unfactored for at least 1 year. It could have been factored by now. Why isn't it factored yet?
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Old 2011-12-16, 18:57   #2
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Do the main 10- tables in the Cunningham Project go over 10^400?
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Old 2011-12-16, 18:58   #3
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I found it here:
http://www.factordb.com/index.php?id...00000013095705

It's also on other sites such as this one:
http://homepage2.nifty.com/m_kamada/math/11111.htm

They're factoring repunits and near-repdigits, but they haven't factored that c166. Why?

Last fiddled with by Stargate38 on 2011-12-16 at 19:01 Reason: Added another site.
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Old 2011-12-16, 19:05   #4
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Quote:
Originally Posted by Stargate38 View Post
...They're factoring repunits and near-repdigits, but they haven't factored that c166. Why?
Because it is relatively hard -
http://homepage2.nifty.com/m_kamada/...ds.htm#BIGGNFS

There are more wanted similar-sized projects.

Last fiddled with by Batalov on 2011-12-16 at 19:15
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Old 2011-12-16, 19:08   #5
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Is anyone ever going to SNFS this number? It's small compared to most number factored by SNFS during the past year. It wouldn't even take a year to GNFS. Anyone have a good poly?

Last fiddled with by Stargate38 on 2011-12-16 at 19:17
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Old 2011-12-16, 19:18   #6
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Ever? I have no doubts about it. 2013, 2014, by almost anyone while doing school homework in parallel.
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Old 2011-12-16, 20:51   #7
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Quote:
Originally Posted by Stargate38 View Post
Is anyone ever going to SNFS this number? It's small compared to most number factored by SNFS during the past year. It wouldn't even take a year to GNFS. Anyone have a good poly?
What kind of resources do you have access to? It will take about one CPU-year to GNFS; so a season if you've got a quad-core, or a month on a fairly heavy (dual six-core Xeon) workstation. msieve and gnfs-lasieve4I15e have been tested thoroughly in this sort of size range; you are unlikely to run into unforeseen road-blocks. You can likely do it yourself, it's a bit big as a first factorisation project but entirely practicable. Feel free to ask any of us for advice.
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Old 2011-12-16, 22:16   #8
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I don't have my computer on 24/7. I have a dual-core AMD Athlon and the longest factorization I've ever done is about 100 minutes on a 91 digit number using SIQS. How do you calculate the time that it takes for NFS factorization? I need an equation. I can't keep my computer on 182.5 days (365 days split between dual-core) nonstop because I get bad storms, on average every 90 days year-round. How long would NFS@Home take to factor it? They do Cunningham numbers all the time.

Last fiddled with by Stargate38 on 2011-12-16 at 22:20
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Old 2011-12-16, 22:47   #9
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Yes they do. But this is not a Cunningham number!

On Kamada's site, you will find some useful plots ...and even a formula.
(Of course, it is for a general estimate only and for any individual set of computers, the estimate may be within ~1/3x to ~3x)
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Old 2011-12-16, 22:53   #10
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NFS@home could probably do it overnight, but it's not big enough to be worth using their resources on; it's the same sort of question as 'how quickly can you get to the shops by space-shuttle', where the answer is 'it would be daft to go to the shops by space-shuttle'.

Sieving is a perfectly parallel process, which means you can do it in almost arbitrarily small chunks and you will lose only small quantities of work with each power outage.

I fear you don't really have enough compute power to do this job without getting frustrated: you really need to be running 64-bit Linux, if only in a VM; you really need 8GB or so of memory; more than two cores would be great.

How do you calculate the time for GNFS? Well, you do a lot of factorisations and fit a curve. I've done a lot of factorisations and fitted a curve, and get

about 100 CPU-hours for 130 digits
multiply by three for every ten digits after that
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Old 2011-12-17, 00:49   #11
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I only have 4 GB of RAM (can't afford to buy more ), along with the pagefile. Is a team sieve possible? I've seen it done with other numbers (ie. numbers from Aliquot Sequences).
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