Current Effort

[fivemack]

Originally Posted by Raman

It is too early for me to reserve for my next number... But I am asking so...
Is 6,335+ faster by using SNFS or GNFS? In case, it is easy by using GNFS, I don't take it up for my next number...
Also that 6,341- even if it is using only a quintic (since it is a multiple of 11), it is rather of difficulty much higher, at 241.23, than 6,343± or 6,335±?

6,335+ is I think easier by SNFS than GNFS; it'd be very similar difficulty to 2^860+1, I would say about eight to ten weeks on four cores of a Q6600 under 32-bit Windows.

6,341- is quite a hard number - harder than I'd want to do on my own. With the right parameters it's probably three months using the 64-bit sievers on a Q6600, or six to eight months using 32-bit ones.

[R.D. Silverman]

Originally Posted by Raman

From my side 6,343+ is 33% sieved so far. Could be relatively faster if the power is more reliable.

Why doesn't someone go on so for 11,229-? It has been standing within the wanted lists for nearly 3 years of time. FactorEyes? No response for that after your last post in Now What (IV) in the factoring forum?

Also that, someone could thus take up for 3,509+ after its twin 3,508+ gets completed up...

It is too early for me to reserve for my next number... But I am asking so...
Is 6,335+ faster by using SNFS or GNFS? In case, it is easy by using GNFS, I don't take it up for my next number...
Also that 6,341- even if it is using only a quintic (since it is a multiple of 11), it is rather of difficulty much higher, at 241.23, than 6,343± or 6,335±? Difficulty = log₁₀(6^310).

Otherwise, I rather think of taking the two left over, remaining candidates for my next numbers, thus either 7,393+ or 10,339+

2,1105-     c158    Zimmermann et al.
5,403-     c159    Womack gnfs
3,527-     c160    Kruppa snfs
2,1012+     c163    Womack+Dodson gnfs
6,311-     c168    CWI (Timofeev) gnfs
6,335-     c170    Silverman
2,865+     c178    Silverman
2,1157-     c182    Kleinjung
6,343+     c191    Raman
2,1606M     c194    Al Edwards
12,259+     c194    Batalov+Dodson
2,859-     c203    mersenneforum+Womack snfs
11,259-     c216    Batalov+Dodson
7,319+     c224    NFSNET
12,256+     c228    Womack+Dodson snfs
11,241+     c242    Buhrow snfs
2,1682L     c245    Batalov+Dodson snfs
7,304+     c244    NFSNET
6,347-     c249    Womack+Dodson snfs
10,393+     c253    Batalov+Dodson
5,383+     c267    Childers/Dodson
2,2086M     c268    Batalov+Dodson snfs
2,908+     c268    Childers/Dodson

Do 7,393+; it will be the easist.

[R.D. Silverman]

Originally Posted by R.D. Silverman

Do 7,393+; it will be the easist.

Other easy numbers include:

6,762M
2,2106L
2,1694M
7,396+

[fivemack]

Ah yes, 6,762M may well be the easiest Cunningham-table number at the moment - a quartic, but the difficulty's actually under 200, so it's not a hard SNFS at all.

Nor a terribly hard GNFS, of course; I'm having surprising success (under 4500 CPU-hours for a C159, estimate under 9000 for a C163 after very little polynomial-search effort) using rather low large-prime bounds, rather large sieve regions, and the very skewed polynomials produced by msieve with small A5. See write-up for the C159 which (fingers crossed) will be on Gratuitous Factors by Sunday night.

[Batalov]

...and 5,370+ and 5,745L to round up the easy list.
...6,340+, 10,530L/M...
Many neglected quartics.

[Raman]

Originally Posted by fivemack

6,335+ is I think easier by SNFS than GNFS; it'd be very similar difficulty to 2^860+1, I would say about eight to ten weeks on four cores of a Q6600 under 32-bit Windows.

@ fivemack: Do you have the parameters that you used so for 2,860+ under GGNFS, the factor base limits, large prime bounds, skew values, (a/r)lambda values, the values for mfb(r/a), etc.

To everyone:
Is it still difficult to tackle 2,1061- by SNFS? It is already 2009! Don't we have enough resources? Even if it is feasible to do sieving by the whole forum, a year round, doesn't someone have the resources to do so with the Linear Algebra atleast in parallel? M1039 was done by Kleinjung, et. al. in May 2009, can't we use the same software for Linear Algebra, (or try to supply the relations to them)?

Seems that Mr. Bruce Dodson has a lot of computers in his university, I think so of. If it is feasible, such a connection of about 100 closely coupled computers will be sufficient to do the LA for a maximum of only 3 months of time period, provided that perhaps someone has it up so, thus.

No small ECM factors at all for 2,1237- and 2,1277- tested so far. They both have been tested upto atleast t60? Similarly, also for the subsequent Mersenne Numbers with no known factors at all too...

[fivemack]

Parameters for 2,860+ were: alim=12M rlim=60M, skew=1 (possibly not optimal), rlambda=alambda=2.6, lpbr=30 lpba=29, mfbr=60 mfba=58, sieved 42M-60M with gnfs-lasieve4I15e. Use these as a starting point rather than taking them as proclaimed truth.

2^1061-1 is still hard, even with Batalov's mods to make lasieve4I16e work; it's too big for a 65536x32768 per-lattice search region to be optimal, so you need a 131072x65536 search region, and the current siever code really wants the coordinates for hits to fit in two bytes which doesn't work in that case. It could be fixed but there are two or three numbers accessible with Batalov's tweaked 16e siever that I'd want to do first, at twenty CPU-years apiece plus three months per number on my i7 machine.

The Kleinjung team (probably better called the Lenstra/Aoki team for M1039) is I suspect still rather tied up with RSA768, and I doubt they have a hundred spare computers for two months in order to push the SNFS record twenty bits further.

[jasonp]

There is no way that msieve in its current form can handle the postprocessing for M1061. Just about everything would have to change: relations cannot exceed 4G, large primes must be <= 32 bits in size, and even Bruce and Greg's machines would be hard-pressed to fit the resulting matrix into memory. Modifying the linear algebra to work on a cluster is left as an exercise to the reader.

[bdodson]

Originally Posted by Raman

Seems that Mr. Bruce Dodson has a lot of computers in his university, I think so of. If it is feasible, such a connection of about 100 closely coupled computers will be sufficient to do the LA for a maximum of only 3 months of time period, provided that perhaps someone has it up so, thus.

Let's remind ourselves of M1039. Importing from one of the reports,

[Linear algebra]
Input matrix:
66 718 354 * 66 718 154 (total weight 9 538 688 635)
Algorithm:
block Wiedemann with 4*64-bit block length
Environment:
110 * Pentium D [3.0GHz], Gb Ethernet, located at NTT
36 * Dual Core2Duo [2.66GHz], Gb Ethernet, located at EPFL
Time:
scaled to 59 days on 110 * Pentium D [3.0GHz] = 36 core years
or 162 days on 32 * Dual Core2Duo [2.66GHz] = 56 core years
...

Calendar time for block Wiedemann was 69 days. Most of the jobs were
done at NTT and EPFL in parallel. However, there were some periods
where no computation took place. Eliminating these periods the
computation could have been done in less than 59 days.
Finally, we got 50 solutions which gave via quadratic character
tests 47 true solutions.

We're using block Lanczos, not block Wiedemann. Check out that
matrix; 66.7M^2, we're not anywhere near that. The pc's had 4Gb/core,
and the network isn't like our generic "whitebox". I'm sieving. No data
exchange between processors during the computation. For a better
comparison on the linear algebra, the number of "threads" was 110 at
NTT, or 36 (or is that 36x2?) at EPFL. With the hardware Tom and
Serge are using, we're currently at 4 threads (a totally bogus comparison,
the BW isn't using threads ...). Compare also this current snfs record with
the gnfs record RSA200, for which they had

...matrix with 64e6 rows and columns,
having 11e9 non-zero entries. This was solved by Block-Wiedemann.
...
The matrix step was performed on a cluster of 80 2.2 GHz Opterons
connected via a Gigabit network and took about 3 months.

Perhaps it's worth noting that the snfs matrix looks (roughly) in the
same range as the gnfs matrix --- both big, I was expecting to be
able to see the snfs1024 matrix being harder (it was, yes? ...). Too
large to be done at a single site (sustained access to fast network),
distributed across two sites. Anyway, Tom/mersenne forum hit
gnfs180, as compared with gnfs200; and we're around snfs difficulty
274, as compared with c. 310. Actually, we're making better relative
progress than I'm seeing in rsa200 --> snfs1024; anyone expect that
we'll see RSA786 this year ... we can have a more current data point
to see where matrix and sieving are ... sieving was done already some
time ago, and the matrix has been grinding away for a year or so? -bd

[frmky]

Is it too early to put in a Christmas wish? I'd love a distributed (MPI would be fine) block Wiedemann implementation this year. Patrick Stach was working on implementations for both for Linux x86-64 and nVidia CUDA, but he seems to have vanished around January. The ability to read msieve mat files would be a plus, but I'm willing to create a conversion program if necessary. The hardware I have access to here includes an nVidia Tesla S1070, an 8-way quad-core Opteron shared memory system, and a 10 quad-core Core2 mini-cluster connected by gigabit ethernet. Pretty please?

[Batalov]

"As I walk through the valley where I harvest my relns
I take a look at my matrix and realize she's very plain
But that's just perfect for an Amish like me
You know I shun fancy things like B-Wee..."