3-2_461 finished
 

The factorisation of 3^461 - 2^461's C141 cofactor is
[code]
P63 96786066288990716928274295383101258082577987291543535344669947 *
P78 104422412340566418572994455302439205048109534911783521862178922442634931037841
[/code]

Polynomial pair used was
[code]
n: 104086805629360160386764643327339530947164392516991460789538108216262911212486335865332754509729901328265550292093903618140476129096312464427
type: gnfs
skew: 191420.76
c5: 5485500
c4: 3618932274822
c3: -1295952956489782834
c2: -59956642229670381330239
c1: 14516941485004310522820179706
c0: 785289125298891646549849485473469
Y1: 7376342316569303
Y0: -452517061343423521410818410
[/code]

with an unusually high Murphy score of 22.2e-12

Large prime bound 2^28 both sides, small prime bound 10^7 both sides.

Sieved Q=5e6 .. 15.571e6, producing 16705251 relations of which 13638558 unique.

Timings: polynomial search about 60 Core2-2.4GHz-hours with pol51m0b and pol51opt, sieving about 850 CPU-hours with gnfs-lasieve14e between 20 June and 1 July on four cores (2xCore2, 2xK8). Constructing 1456677 x 1456925 matrix with weight 108274040 took about 30 minutes on one Core2-2.4GHz; linear algebra with two threads took five hours on two cores Core2-2.4GHz; each square root took fifty minutes. This stage was done with msieve.

[QUOTE=Andi47;109394]@Paul:

A small bug (or two) crept into the update file:

I found the factors of 7,2,286+ c96 and 7,2,207+ c98 with ECM, not MPQS, the only factor which I found with QS yesterday was the factor of the remaining 7,2,207+ c76.

P.S.: What does the statement in this line (bold font) in the update file mean?

[code]7+2 207 C76 [b]10952371395236857209217+2 7438098391.[/b] P43 A Schindel MPQS 2007-06-30[/code]

I guess, this line is intended to say "1095237139523685720921757438098391*p43"?[/QUOTE]Thanks for letting me know. It's not surprising that a bug or two crept in. I'll fix the ECM/MPQS confusion.

The bold line means that two lines were concatenated in error. I'll sort it out.


Paul

New numbers merged into the reservation server
 

At
[url]http://www.chiark.greenend.org.uk/ucgi/~twomack/homcun.pl?sortby=snfs[/url]
you will notice a whole load of new numbers, waving their digits in the breeze and waiting to be harvested.

[QUOTE=Andi47;109394]I found the factors of 7,2,286+ c96 and 7,2,207+ c98 with ECM, [/QUOTE]
You mean 7,2,186+ c96 --- see how easy it is to make errors?:wink:

Paul

[QUOTE=xilman;109403]You mean 7,2,186+ c96 --- see how easy it is to make errors?:wink:

Paul[/QUOTE]

Oooops.... :wink:

Well ,I've made the complete factorization of C103 in 2,7,201+ (only now I understand,that this number is reserved by other man, according to [URL]http://www.chiark.greenend.org.uk/ucgi/~twomack/homcun.pl?sortby=snfs;[/URL] I hope he will excuse me :) ). Nevertheless, factorization was done with ecm 6.1 at b1=80000000 for 4 hours. c103= 1987053219650038636440057116498758283079373 (43 digits)* 1571904486412266685573982376240822330077441948160296840379697 (61 digits). Both proved to be prime by certified with primo 3.0.2 and ProvablePrimeQ (Mathematica 6.0)

[QUOTE=VolMike;109441]Well ,I've made the complete factorization of C103 in 2,7,201+ (only now I understand,that this number is reserved by other man, according to [URL]http://www.chiark.greenend.org.uk/ucgi/~twomack/homcun.pl?sortby=snfs;[/URL] I hope he will excuse me :) )[/QUOTE]

That's me, I have also posted the reservation in this thread (here: [url]http://www.mersenneforum.org/showpost.php?p=109360&postcount=432[/url] ).

I excuse You, but please check for reservations next time.

I will reserve an other number tonight. (I was halfway through QS'ing 2,7,201+, but I have shut down my computer at home due to heavy thunderstorms at my location predicted for today in the afternoon.)

[quote=Andi47;109443]That's me, I have also posted the reservation in this thread (here: [URL]http://www.mersenneforum.org/showpost.php?p=109360&postcount=432[/URL] ).

I excuse You, but please check for reservations next time.

I will reserve an other number tonight. (I was halfway through QS'ing 2,7,201+, but I have shut down my computer at home due to heavy thunderstorms at my location predicted for today in the afternoon.)[/quote]

Ok. Nowtime I know about link for reservation and then it will be no mistake.

[QUOTE=fivemack;109070]Eight years from needing a $10M Cray to needing a $400 desktop is an awful lot faster than Moore's Law would suggest, though I suppose the right deduction from that is that you didn't need something as big as the Cray ... indeed, after a bit of digging [...] an AlphaServer DS20 was available at the time and could hold even 4GB of RAM. But nine days on one CPU of what I think was then a fairly elderly Cray was probably easier to come by than a month on the whole of what was then a new high-end server.[/QUOTE]

Two years for Cray 1999 to Origin 2001, the first large-scale use of parallel
Lanczos, 25 cpus. There were lots of Origins (we had one), but the binary
wasn't (and isn't) public. Paul Leyland's pc cluster version (MSR) was around
the same date. -Bruce

cf Peter's nmbrthry post, extracted at
[url]http://www.lehigh.edu/~bad0/msg06332.html[/url]
The code was 1999-2001, but the hardware wasn't up to the
task --- Peter made a preliminary report at an RSA conference, which
Bob referred to (for some years) as evidence of poor cpu usage in the
parallelization -- but this Sept 2001 date is our benchmark for the
parallel matrix version. Of course, the issues have shifted now that
Franke's Wiedermann distributes the matrix computation.

Postscript. Still on the parallel Lanczos, if one insists on record
computations, that would be the matrix for M809 --- Franke's
report (Contini's page) notes the matrix (and some line sieving)
done CWI --- the Origin code --- although lattice sieving and
the rest of the post-processing was at Bonn. First details (that
I heard) were at the Utrecht workshop, Franke's talk; which also
described the matrix for RSA160 and the just completed RSA576;
3 big matrices, all parallel block Lanczos. Peter mentioned sieving
for M809 (with larger large primes) was done already in the spring;
but the record was delayed due to disk space requirements at
Bonn. None of these are Cray issues; not to put too much emphasis
on a fine point. -bd

I suppose my question is "how large a number can you handle with today's public software and a single 4-core 8GB machine running for six months".

The impression I have is that that would be just about enough to handle the matrix from Aoki's 176-digit GNFS, and a bit small for their 274-digit SNFS.

4-core 8GB machines are startlingly cheap (I don't know whether the bottom has dropped out of the RAM market permanently or temporarily, but 2GB modules are under £65 at the moment); a cluster of four of those would cost about six thousand dollars and probably would happily handle a few 900-bit SNFS matrices a year, but the matrices are growing very quickly as you get to the kilobit level: the minimal system for storing the M1039 matrix would be nine 8GB machines, and would have to run for about a year.

I don't know if there's enough sieving being done out there to keep a four-machine linalg cluster busy.

[QUOTE=VolMike;109441]Well ,I've made the complete factorization of C103 in 2,7,201+ (only now I understand,that this number is reserved by other man, according to [URL]http://www.chiark.greenend.org.uk/ucgi/~twomack/homcun.pl?sortby=snfs;[/URL] I hope he will excuse me :) ). Nevertheless, factorization was done with ecm 6.1 at b1=80000000 for 4 hours. c103= 1987053219650038636440057116498758283079373 (43 digits)* 1571904486412266685573982376240822330077441948160296840379697 (61 digits). Both proved to be prime by certified with primo 3.0.2 and ProvablePrimeQ (Mathematica 6.0)[/QUOTE]

Have you emailed your result to Paul (Xilman)?