P1365

[themaster]

i just stumbled across this
http://www.euronet.nl/users/bota/medium-p-odd.txt

[xilman]

Originally Posted by themaster

i just stumbled across this
http://www.euronet.nl/users/bota/medium-p-odd.txt

Unfortunately, that leaves just the C145.

I was unable to find any known factors either. I recommend a cpu-month or so of ECM and then turn to GNFS.

Paul

[themaster]

i will do that
7-zip is unable to decompress factors.gz on this site could someone point me to a program that will
http://web.comlab.ox.ac.uk/oucl/work...t/factors.html

[fivemack]

I have just bought what seems close to a ridiculous superabundance of compute power; unless someone else is doing it already, I'll do the gnfs.

Tom

[R.D. Silverman]

Originally Posted by fivemack

I have just bought what seems close to a ridiculous superabundance of compute power; unless someone else is doing it already, I'll do the gnfs.

Tom

What is the importance of this number?

Congratulations on your recent riches.

I have a total of only about 16 cores on a given night.

[fivemack]

What is the importance of this number?

If I think too hard about that, I quickly come to the conclusion that there is no importance in any number, and that I should devote my resources (two Q6600 boxes and a dual-core AMD, so ten cores, but relatively fast ones) to some more worthy cause - the Rosetta@home protein-folding project seems to have about 30% success rate at getting protein structures close enough for crystallographic use, albeit at a cost of 10,000 CPU-years per attempt, 99.999% of which is wasted exploring regions of conformation space where the protein isn't. My friends think I am somewhat odd to have factorisation as a hobby; maybe I should believe them.

From the shape of the silences in the gossip at SHARCS 2007, and a couple of timescale observations - 200 Opteron-years for the sieving step - announced in the talks over what were rather generic slides, with high probability RSA768 will be factored sometime this year; this will get into the middle pages of reputable newspapers for a day.

There is probably virtue in thinking about the triplication formula for Perrin numbers, and whether there's some meaningful way in which you can combine points with { f(x,y,z), x-A, y-B, z-C } smooth in an index-calculus fashion; but I'm not sure I have enough brain and enough drive to get much out of the 'inhale Hartshorne on Algebraic Geometry' first step, and anyhow this is the sort of thought that can be done in a quiet library while the computers crunch away elsewhere. I can't help thinking that, if by implausible chance I can get myself into book-inhaling mode, I might not be better off in two senses by inhaling Paul Willmott on quantitative finance instead.

[bdodson]

Originally Posted by fivemack

... and a couple of timescale observations - 200 Opteron-years for the sieving step - announced in the talks over what were rather generic slides, with high probability RSA768 will be factored sometime this year; this will get into the middle pages of reputable newspapers for a day.

Fox noise network aside, if one regards the NY Times as reputable, the
RSA512 reporting stretched over a week. That being in the business
section, along with updating the DOC review of allowing larger key_sizes
for international e-commerce. So if someone concludes that RSA1024 is
next after RSA768 (true), and misses the effect of the ratio of the runtimes
L(1024)/L(768), they might conclude that 1024-bits is no longer secure
(perhaps true, as well?), and there might be a somewhat longer flurry of
reporting. Given the larger available memory for sieving, no one should be
surprized at the 768-bit sieving; the interesting part will be seeing how
distributed Wiedemann scales (up from the 1024-kilobit snfs matrix).

There is probably virtue in thinking about the triplication formula for Perrin numbers, and whether there's some meaningful way in which you can combine points with { f(x,y,z), x-A, y-B, z-C } smooth in an index-calculus fashion; but I'm not sure I have enough brain and enough drive to get much out of the 'inhale Hartshorne on Algebraic Geometry' first step, ... I can't help thinking that, ... I might not be better off in two senses by inhaling Paul Willmott on quantitative finance instead.

If I read correctly, JasonP was noting the post_processing steps of
nfs in Franke et.al.'s suite as a milestone. I was mutering to myself about
Peter's version of BLanczos, and the sqrt; as well as the Lenstra/Manasse
(F9 by email, snfs512) and Lenstra/Bernstein (maspar) precursors. But
99.9% of mathematicians know Franke's name/reputation for his
acomplishments in Grothendiek/Deligne AG. We had a colloquim here last
year from one of the current stars describing recent analytic work, and
grumbling that his new methods gave new proofs, but no better results from
what Jens had a decade earlier; I looked as some of the papers, back in the
day, real serious inhaling, way beyond Hartshorne first steps. -Bruce

[henryzz]

according to his first post this number is a factor of M13# (M30030)
so as far as mersenne exponents go it might be a nice one to factor

[jasonp]

Bruce, I only commented on the postprocessing not because it was a milestone, but just because the amount of work involved was so large for the filtering, a stage that mere mortals complete in two hours on a single machine, that they had to throw 100+ machines at it and it still took days. I'm not used to thinking of SNFS job size in terms like that.

Also, I suspect that the 512-bit news was news for so long because US law at the time required key sizes no larger for exportable cryptographic products. For all I know it still does, albeit with exceptions made more easily now if you're a bank or other large entity.

Tom: I post this link regularly now. No reasons or nobility of purpose are needed in deciding how you spend your computer or human time. I console myself that no choice I make will bring about world peace, so it may as well be something I enjoy, even if the resons for that enjoyment are somewhat inscrutable. And while I spend much of my spare human time on factoring, my one always-on machine has been running climateprediction.net since that project started.

[fivemack]

The C145 of P1365 splits as

P54 307125743850143133483913160596928028514251505520546641

P91 5688731769073295226822443339772781659917616096118503020829580687650366528080737234892225491

(GNFS; started polynomial search 2300 11 January, got a good candidate by 1745 13 January, sieved 15/1 9:40 to 20/1 1900 on up to ten cores, then four runs of msieve on unreliable hardware which failed, and final success at 15:45 27 January)

Polynomials

BEGIN POLY #skewness 123379.67 norm 6.42e+19 alpha -5.24 Murphy_E 9.21e-12
X5 3385200
X4 8661484321648
X3 -618651246328596650
X2 -23986786701021637799387
X1 4552597702340635731023948748
X0 -23917562434897885776075583536864
Y1 41282500734453253
Y0 -3487761976463661427576906001

29-bit large primes, small primes above 20M, sieved with gnfs-lasieve14e, 42897129 relations of which 39861829 unique, nice easy matrix solved in 48 hours on one CPU

Fri Jan 25 10:09:57 2008  matrix is 3669520 x 3669713 (1035.3 MB) with weight 340776896 (92.86/col)
Fri Jan 25 10:09:57 2008  sparse part has weight 227350645 (61.95/col)
Fri Jan 25 10:09:57 2008  saving the first 48 matrix rows for later
Fri Jan 25 10:09:59 2008  matrix is 3669472 x 3669713 (997.8 MB) with weight 260809339 (71.07/col)
Fri Jan 25 10:09:59 2008  sparse part has weight 224871607 (61.28/col)
Fri Jan 25 10:10:26 2008  memory use: 959.8 MB
Sun Jan 27 10:47:04 2008  lanczos halted after 58027 iterations (dim = 3669457)

Result on the second dependency at 2.5hrs/dependency.

Should I email this, or is the maintainer of the small-Mersenneish-factors list likely to be reading this group?

[xilman]

Originally Posted by fivemack

Should I email this, or is the maintainer of the small-Mersenneish-factors list likely to be reading this group?

Nice one.

I'd email it. Can't hurt and I, for one, prefer to receive factors by email rather than being expected to scrape them from a forum.


Paul