73 digit ECM factor - Page 9

Batalov · 2010-11-24, 00:20

It appears that they sweeped once to the top (and even beyond with M1237) and started again from the bottom with another set of parameters (and/or ideas!).

R.D. Silverman · 2010-11-24, 15:12

Sam Wagstaff just found a P69 factor of 3^1443+1.

CRGreathouse · 2010-11-24, 15:37

Quote:

Originally Posted by R.D. Silverman

Sam Wagstaff just found a P69 factor of 3^1443+1.

What is it? I trust this completes the factorization.

R.D. Silverman · 2010-11-24, 15:45

Quote:

Originally Posted by CRGreathouse

What is it? I trust this completes the factorization.

It is available on the ECMNET 'latest' webpage. I did not extract its
value.

Batalov · 2010-11-24, 19:03

That's a very nice factor. Now, I am pretty sure that my p63 won't survive top-10 for the year. Which is pretty impressive if we compare top-2010 to top-2009 for example.

P.S. Note that base 3 PRP test is no good for these 3+ and 3- extensions. It is easy to step into it. For example, the c204 composite cofactor for 3,748+ is a 3-PRP. But this 3,1343L c154 factorization is indeed complete.

R.D. Silverman · 2010-11-24, 19:14

Quote:

Originally Posted by Batalov

That's a very nice factor. Now, I am pretty sure that my p63 won't survive top-10 for the year. Which is pretty impressive if we compare top-2010 to top-2009 for example.

P.S. Note that base 3 PRP test is no good for these 3+ and 3- extensions. It is easy to step into it. For example, the c204 composite cofactor for 3,748+ is a 3-PRP. But this 3,1343L c154 factorization is indeed complete.

Please note that 3^k+1 is going to be a 3-PRP......

Batalov · 2010-11-24, 19:36

Of course. As well as Eisenstein Mersenne norms, and GFN3'. There was a storm in a glass of water in the corresponding OEIS sequences once...

Raman · 2010-11-24, 21:42

Quote:

Originally Posted by R.D. Silverman

Sam Wagstaff just found a P69 factor of 3^1443+1.

I want to know, why this number was being done by using ECM, after such an extended effort. After all, this number was only 154 digits, could have been done so by using GNFS. Was it really ECM, first of all? Or that was it an arbitrary sigma, B1 values that was being entered into that factor form as ECM, rather? ;-) In my opinion, clearly that for now ECM time could be spent upon that much harder candidates.

@bdodson: I have released with 10,590M 2,985- for now. You may feel free to reserve it up. (If you wish to do so - if it was the case that you had with these two numbers as an active target before itself). They certainly require with gnfs-lasieve4I16e lattice siever, that takes up with more memory. I am concentrating upon 2,2334M 2,1930M 2,2334L sieving at this moment. If they go unreserved, then rather I will take them up depending upon my availability of resources, a few more months later on.

bdodson · 2010-11-24, 22:54

Quote:

Originally Posted by Raman

I want to know, why this number was being done by using ECM, after such an extended effort. ...

Sam reported a bunch of ecm factors from the 3+ extension using
B1 =350M. I don't see evidence of a test to p60 having been completed;
and am still running short tests with p60-limits, submitting 5700 curves,
B1 = 260M (c. 3t50 << t55) on the numbers Sam's promoted from the
3- extension to the regular Cunningham tables.

There was a previous factor from Sam using B1 = 500M. I'm guessing that
he ran a few curves on each number in the 3+ extension, then bumped his
limits up to the B1 = 600M used to find this p69 (the very first found by
ecm, and record for non-PS3 ecm!). Unless you have some reason to
believe that there were 10,000s of curves run on this C154?

Quote:

... In my opinion, ...

@bdodson: I have released with 10,590M 2,985- for now. You may feel free to reserve it up. (If you wish to do so - if it was the case that you had with these two numbers as an active target before itself). They certainly require with gnfs-lasieve4I16e lattice siever, that takes up with more memory. I am concentrating upon 2,2334M 2,1930M 2,2334L sieving at this moment. If they go unreserved, then rather I will take them up depending upon my availability of resources, a few more months later on.

Thanks, I noticed that these went from reserved "Raman" to being still
listed on Sam's "who's factoring" page, but open to whoever wants them
soonest. I think that you've complied with Bob's comment on your number
reservations being more than you'd be able to do in a month or two. I wasn't
clear whether he intended to try sieving these specific numbers; and
believe I recall that he was considering switching to ecm, if they were too
difficult.

So far as I've heard, I don't think that Serge would consider reserving these
numbers for B+D if there's still a chance that you'll be able to get to them
(including doing the matrix) before your current resources time out. We
still have the more wanted 5p394 that's available in our current range; and
I expect to be sieving 5p397 (snfs) and Tom's 2p956 (gnfs) for some time.

-Bruce

Batalov · 2010-11-24, 23:31

Or maybe, just maybe, Sam is using his grandson's PS3...

...just kidding.

These quartics are fairly unappealing. There's now a backlog of obligatory quintics, too, that no one wants to touch with a 20-ft pole. There's one that we could possibly do, but Bruce signed up for a O(weeks) chunk of the 2,956+ sieving. (I sieve for it too in the meantime, you are going to be laughing!)

Raman · 2010-11-25, 07:06

There has been a lot of work out of my own fancy that has been stalled for past few years because that had been boring for a while (maybe that was due to concentration upon Cunningham project?)
that I would rather plan to compile it into my own website, which I would rather expect it to be ready within a time period of two years or so. I came up with that idea of having my own website only a few months ago, so that its construction process has not yet begun, so far, still at this moment.

As of now, for that two numbers 10,590M 2,985- besides requiring with that gnfs-lasieve4I16e lattice siever, thus taking (consuming) up with more memory, that matrix takes probably upto 2.5 months in order to solve, unless parallelized in which case it takes upto only a bit lesser amount of time period, actually.

Plus, that I must remind about the fact that the compute cluster resources should have to be renewed at this end of one year time scale, rather.

2010-11-24, 15:12	#90
R.D. Silverman Nov 2003 2²×5×373 Posts	P69 Sam Wagstaff just found a P69 factor of 3^1443+1.

2010-11-24, 19:03	#93
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 22420₈ Posts	That's a very nice factor. Now, I am pretty sure that my p63 won't survive top-10 for the year. Which is pretty impressive if we compare top-2010 to top-2009 for example. P.S. Note that base 3 PRP test is no good for these 3+ and 3- extensions. It is easy to step into it. For example, the c204 composite cofactor for 3,748+ is a 3-PRP. But this 3,1343L c154 factorization is indeed complete. Last fiddled with by Batalov on 2010-11-24 at 19:13

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Factor a 108-digit number	sweety439	Factoring	9	2016-12-21 21:22
New 70 digit factor	R.D. Silverman	Cunningham Tables	16	2016-01-23 22:16
44-digit factor found using ECM w/ B1=1e6 & B2=1e8	WVU Mersenneer	Factoring	8	2010-04-24 17:01
Probability of n-digit factor?	roger	Factoring	3	2007-05-09 22:51
160 digit factor found of 366 digit (PRP-1)	AntonVrba	Factoring	7	2005-12-06 22:02

2010-11-24, 00:20	#89
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2⁴·593 Posts	It appears that they sweeped once to the top (and even beyond with M1237) and started again from the bottom with another set of parameters (and/or ideas!).

2010-11-24, 19:36	#95
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2⁴×593 Posts	Of course. As well as Eisenstein Mersenne norms, and GFN3'. There was a storm in a glass of water in the corresponding OEIS sequences once...

2010-11-24, 23:31	#98
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2⁴×593 Posts	Or maybe, just maybe, Sam is using his grandson's PS3... ...just kidding. These quartics are fairly unappealing. There's now a backlog of obligatory quintics, too, that no one wants to touch with a 20-ft pole. There's one that we could possibly do, but Bruce signed up for a O(weeks) chunk of the 2,956+ sieving. (I sieve for it too in the meantime, you are going to be laughing!)

2010-11-25, 07:06	#99
Raman Noodles "Mr. Tuch" Dec 2007 Chennai, India 3·419 Posts	There has been a lot of work out of my own fancy that has been stalled for past few years because that had been boring for a while (maybe that was due to concentration upon Cunningham project?) that I would rather plan to compile it into my own website, which I would rather expect it to be ready within a time period of two years or so. I came up with that idea of having my own website only a few months ago, so that its construction process has not yet begun, so far, still at this moment. As of now, for that two numbers 10,590M 2,985- besides requiring with that gnfs-lasieve4I16e lattice siever, thus taking (consuming) up with more memory, that matrix takes probably upto 2.5 months in order to solve, unless parallelized in which case it takes upto only a bit lesser amount of time period, actually. Plus, that I must remind about the fact that the compute cluster resources should have to be renewed at this end of one year time scale, rather.