C166 from 10^455-1?

[R.D. Silverman]

Originally Posted by Stargate38

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?

It is ENORMOUS for SNFS!!!!!!!!! It is way beyond even M1061.

[debrouxl]

10,455-, 3,710+ and 3,616+ (I see that 3,608+ has been factored) can be sieved by RSALS, using 14e.
15e would probably be marginally faster (I know that Aliquot team sievings on MersenneForum usually use 15e above GNFS difficulty 163), but RSALS can sometimes yield a factorization more quickly, because it usually has more core than team sievings.

But 3,710+ and 3,616+ might be reserved, or being worked on at the time being ?

[xilman]

Originally Posted by R.D. Silverman

It is ENORMOUS for SNFS!!!!!!!!! It is way beyond even M1061.

I suspect he's comparing the C166 with the C2xx and even C3xx which have been factored by SNFS. Many people here know why that's a false comparison but we all have to learn sometime.

Stargate33: as a rule of thumb, SNFS only works on the full number to be factored, 10^455-1 in this case, and it usually can't exploit any known factors. There are exceptions but it's a good rule of thumb. 10^455-1 has 455 digits and, as Bob says, 455 is much larger than anything yet done by SNFS.

Paul

[Andi47]

Originally Posted by xilman

I suspect he's comparing the C166 with the C2xx and even C3xx which have been factored by SNFS. Many people here know why that's a false comparison but we all have to learn sometime.

Stargate33: as a rule of thumb, SNFS only works on the full number to be factored, 10^455-1 in this case, and it usually can't exploit any known factors. There are exceptions but it's a good rule of thumb. 10^455-1 has 455 digits and, as Bob says, 455 is much larger than anything yet done by SNFS.

Paul

In this case you can divide out the algebraic factor (10^91-1) to get:

n: 4550956748305222152126018815762238940620303956367340855900091266114182783163428849423951840315664063783883817473128035867761145293485421290359307345105428632108260961
skew: 1
c4 1
c3 1
c2 1
c1 1
c0 1 
Y1 1
Y0 -10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
rlim: 500000000
alim: 500000000
lpbr: 35
lpba: 35
rlambda: 2.6
alambda: 2.6
mfbr: 70
mfba: 70
#sieve with the 16e siever for at least a billion relations
#parameters are just a guesstimate

but that's still SNFS-difficulty 365(!) and thus far out of range for home computing. GNFS-166 is waaaay easier (and should doable with a single intel i7 with enough RAM and a user with enough patience.)

[bdodson]

Originally Posted by debrouxl

10,455-, 3,710+ and 3,616+ (I see that 3,608+ has been factored) can be sieved by RSALS, using 14e.
15e would probably be marginally faster (I know that Aliquot team sievings on MersenneForum usually use 15e above GNFS difficulty 163), but RSALS can sometimes yield a factorization more quickly, because it usually has more core than team sievings.

But 3,710+ and 3,616+ might be reserved, or being worked on at the time being ?

This info is available at
http://homes.cerias.purdue.edu/~ssw/cun/who
the "who is factoring ..." page (for Cunningham numbers). We added
3,616+ shortly after finishing 3,608+ (an ecm cofactor). I'm frequently
checking to make sure that I'm not running ecm on numbers someone
else is sieving --- I just recently trimmed 3 of 37 from the extension with
163-233 digits. At the moment, 3,710+ is open. I'm usually sieving
larger/harder numbers (5p237 sieving finished, matrix running; 11p271
paused), and have scripts for 15e and 16e, but not 14e.

Bruce (as in Batalov+Dodson)

[Stargate38]

That must mean that GNFS is faster than SNFS in this case. Is this number on RSALS todo list? If not, I really want it factored as fast as possible. Anyone want to do it? I don't have the 8 GB of memory required. :( What's the fastest way of GNFS'ing this? How do you calculate SNFS difficulty?

[fivemack]

Why do you want this number factored?

To get some order of magnitude of the favour that you are asking, I estimate that it would take between fifteen and twenty days to factor it on my large server, and cost therefore about a hundred dollars in electricity and about fifty dollars in depreciation of the server. If you're willing to pay for that I will drop everything and factor it on my large server, but bear in mind that $150 would buy you the extra memory that you lack.

[wblipp]

Originally Posted by Stargate38

Is this number on RSALS todo list?

How much ECM has been done? I can't speak for RSALS, but they have often factored adequately pre-tested numbers for other projects.

It's customary to do ECM through 1/3 of the number size before GNFS. That is about 24,000 curves with B1=11e7, or 70,500 with B1=43e6, or 10,000 with B1=26e7, or some equivalent combination. Everybody will want that much ECM before GNFS to make it unlikely there are small factors that are more easily found with ECM.

If that sounds like a lot of computing, remember that it is much smaller than the GNFS factoring that you are asking for. Are you sufficiently interested to do the ECM work yourself? If so, then politely ask debrouxl if RSALS would do the GNFS if the ECM fails to find a factor.

[schickel]

Originally Posted by fivemack

Why do you want this number factored?

To get some order of magnitude of the favour that you are asking, I estimate that it would take between fifteen and twenty days to factor it on my large server, and cost therefore about a hundred dollars in electricity and about fifty dollars in depreciation of the server. If you're willing to pay for that I will drop everything and factor it on my large server, but bear in mind that $150 would buy you the extra memory that you lack.

I'd be willing to pay $5 if you factored it and then posted the factors a digit at a time over the course of a week...

[schickel]

Originally Posted by wblipp

How much ECM has been done? I can't speak for RSALS, but they have often factored adequately pre-tested numbers for other projects.

It's customary to do ECM through 1/3 of the number size before GNFS. That is about 24,000 curves with B1=11e7, or 70,500 with B1=43e6, or 10,000 with B1=26e7, or some equivalent combination. Everybody will want that much ECM before GNFS to make it unlikely there are small factors that are more easily found with ECM.

If that sounds like a lot of computing, remember that it is much smaller than the GNFS factoring that you are asking for. Are you sufficiently interested to do the ECM work yourself? If so, then politely ask debrouxl if RSALS would do the GNFS if the ECM fails to find a factor.

I'd run some ECM work for $5 or so (then I could pay Tom.....)

[debrouxl]

ECM up to 1/3 of GNFS difficulty (William's numbers) may be a bit much, but indeed, I wouldn't queue a GNFS 166 to RSALS before it has received, say, half, or two thirds, of t55, i.e. 9000 or 12000 curves at B1=11e7 (or equivalent). That's quite a bit of work...