Updated tables.
 

The tables at [url]http://www.leyland.vispa.com/numth/factorization/anbn/main.htm[/url] have just been updated.

There are now only 73 composites remaining. When this figure falls to 50 or under, I will add some extensions to the tables.

As always, my thanks to those of you who have been finding and submitting factors and those who have sent in corrections for my errors in recording them..


Paul

tiptoeing across the borderline
 

I just put my nose a bit across the current borderline to grab some easy factors (ecm, 77 curves with B1=11k each)

3,2,503- = p5*p12*p13*c212

p5 = 51307
p12 = 430851407303
p13 = 2478754360223


3,2,509- = p6*p7*p12*c220

p6 = 544631
p7 = 1121837
p12 = 154685075569


3,2,521- = p5*p8*p19*c219

p5 = 47933
p8 = 12951019
p19 = 1081649584929776563


3,2,523- = p4*p11*p11*c225

p4 = 5231
p11 = 39579233131
p11 = 52933182503


3,2,541- = p5*p7*p18*p230 (completely factored)

p5 = 11903
p7 = 3073963
p18 = 536810152868180251
p230 = 67518535351625284953826953974871481207814944259904665785817984189151153006919359709652835593880167358883587106160961656805965726563782426951051332719350359065180577251346354781858299582543330199863357312952793569420983972972416709

p230 cofactor certified prime with primo

[QUOTE=Andi47;105886]I just put my nose a bit across the current borderline to grab some easy factors (ecm, 77 curves with B1=11k each)

3,2,503- = p5*p12*p13*c212

p5 = 51307
p12 = 430851407303
p13 = 2478754360223


3,2,509- = p6*p7*p12*c220

p6 = 544631
p7 = 1121837
p12 = 154685075569


3,2,521- = p5*p8*p19*c219

p5 = 47933
p8 = 12951019
p19 = 1081649584929776563


3,2,523- = p4*p11*p11*c225

p4 = 5231
p11 = 39579233131
p11 = 52933182503


3,2,541- = p5*p7*p18*p230 (completely factored)

p5 = 11903
p7 = 3073963
p18 = 536810152868180251
p230 = 67518535351625284953826953974871481207814944259904665785817984189151153006919359709652835593880167358883587106160961656805965726563782426951051332719350359065180577251346354781858299582543330199863357312952793569420983972972416709

p230 cofactor certified prime with primo[/QUOTE]To be honest, you're wasting your time.

I ran a significant amount of ECM on all the extensions last year and found thousands of factors.

Carry on if you wish, but I won't give any credit on the web pages until the extensions are released to the public.


Paul

[QUOTE=xilman;105889]To be honest, you're wasting your time.

I ran a significant amount of ECM on all the extensions last year and found thousands of factors.

Carry on if you wish, but I won't give any credit on the web pages until the extensions are released to the public.


Paul[/QUOTE]

I have stopped after the numbers I posted, so I have wasted only approx. 10 minutes of cpu-time.

After about three CPU-weeks of sieving, and quite a lot of processing attempts,

3^451 - 2^451 = 23^2 * 331 * 821 * 32309 * 56827 * 58631 * 99139 * 13869481 * 1690496411473 * 2514094051921 * 504321986661276694901 * 330101180951681949097644973201458413117182235901050947 P54 * 10092482624886822918824948465636818174309279189631346061405697742235975757536520473 P83

(GGNFS on the product of the two large factors)

Eventual success after increasing the permitted size of intermediate relations files and running procrels over all the relations from scratch; previously it had had a habit of crashing half-way through preparing the matrix. It still breaks msieve-1.21.

[QUOTE=xilman;105880]The tables at [url]http://www.leyland.vispa.com/numth/factorization/anbn/main.htm[/url] have just been updated.

There are now only 73 composites remaining. When this figure falls to 50 or under, I will add some extensions to the tables.

As always, my thanks to those of you who have been finding and submitting factors and those who have sent in corrections for my errors in recording them..


Paul[/QUOTE]Another update just posted, this with 9 more completed factorizations. There are only 14 more to go before I add some extension tables.

Eight of the nine were by NFS, found by Greg Childers and Tom Womack. The other was discovered by Pierre Jammes who used the ECMNET client to find a 41-digit prime factor.


Paul

[QUOTE=R.D. Silverman on a different thread;107260]Allow me to repeat something that I think was orginally said by Dick Lehmer
(but I am not sure of the source)

"The purpose of computing is insight, not numbers".

However, as far as I can tell, the OPN project is just computing for the numbers, and not insight. I see no point in chasing factorizations just so the lower bound on the size of OPN''s can be increased.
[/QUOTE]

I thought it was Hamming's quote.

Since Bob has decided it's time to be asking these questions again, what insight do you hope to gain from this project? If it's been posted, I missed it. The numbers are of such little interest that nobody had previously bothered to name them, and nobody had previously established archives for the factors. You may not approve of increasing OPN bounds, but at least there is a use - I've seen no indication that these factors are useful for anything at all.

At last, a respectably-sized factor
 

After an enormous amount of work by jasonp to get msieve to produce matrices which generate non-trivial dependencies, sixty or so million relations that I'd collected on four CPUs over the course of about a month have been boiled down to

[code]
6^256 + 5^256 = 9040982982437273742755379993064289353404891739205578878208413109886576129 * 1780346136439289107121918177640218009965158927099375999821000196599643512555740683854877929960240542107870215833595988540364289
[/code]

Small factor is a p73, first one I've managed which is larger than the ECM record-holder. This is, with two £200 mid-2007 PCs and free software (a combination of Franke's sieve and Jason's relation processing), comparable to what a large team with a Cray managed at the start of 1999.

I'm not sure whether, in 2015, I should expect to factor a general C200 in a month using two £200 mid-2015 PCs and free software. I'd bet against.

[QUOTE=fivemack;108644]After an enormous amount of work by jasonp to get msieve to produce matrices which generate non-trivial dependencies, sixty or so million relations that I'd collected on four CPUs over the course of about a month have been boiled down to ...

Small factor is a p73, first one I've managed which is larger than the ECM record-holder. This is, with two £200 mid-2007 PCs and free software (a combination of Franke's sieve and Jason's relation processing), comparable to what a large team with a Cray managed at the start of 1999. ...[/QUOTE]

Congratulations. But I'm more than a bit puzzled by your intended
comparison to 1999. Feb '99 was RSA-140; Aug '99 was RSA-155 =
512-bit gnfs. But then your 73+123 = c196 must have been an snfs
(otherwise the appropriate comparison would have been to rsa200, for
gnfs). CWI reports a c186 snfs in '98; then we did a c211 in April '99
by snfs --- so this is the intended comparison? Yours is twice as
hard (by snfs runtime) as the c186, but the c211 is more than twice
as hard as the c196 --- twice to c206, another 3/2 to c211; more
like three times as hard. We reported c211 snfs as being harder than
the 140-digit gnfs, with sieving on 125 "fast workstations" + 60
pcs (Pentium II's; cf the RSA-155 report). Filtering and the matrix
build was done on the SGI Origin (also super), then the matrix on
the Cray, for which the main feature used was 2Gb of fast memory,
on a single cpu. Since this was before 2000 (when MS bought/licensed
the CWI suite), the software was still free (in particular, Lehigh didn't
pay for a complete set of sgi binaries between snfs211 and the start
of rsa-155, when I did my first snfs's. Well, not counting the cycles
spent on rsa-140, snfs-211, rsa-155, snfs-233 (768-bits, Nov. 2000).).
-Bruce

[QUOTE=bdodson;108722]Congratulations. But I'm more than a bit puzzled by your intended
comparison to 1999. ... CWI reports a c186 snfs in '98; then we did a c211 in April '99
by snfs --- so this is the intended comparison?[/QUOTE]

I took an average between the C186 in September 1998 and C211 in April 1999 to get C200 (my number is P73 * P127, I'm not quite sure where the 196 came from) in 'early 1999'; I realize this isn't quite fair since the C211 is significantly harder than C200 and C186 significantly easier, the software and the organisation of resources was coming on by leaps and bounds at the time.

The real factor making it possible to do these things now on cheap hardware, as you point out, is that 2G of fast-enough memory attached to a 64-bit CPU is now supported by a £50 motherboard. Though the software has also got a lot better; the sieving for the C140 I'm running now will take about eight 2GHz-weeks, which I can't get to come out to more than about 500 MIPS-years.

[QUOTE=fivemack;108734]I took an average between the C186 in September 1998 and C211 in April 1999 to get C200 (my number is P73 * P127, I'm not quite sure where the 196 came from) in 'early 1999'; ...

... Though the software has also got a lot better; the sieving for the C140 I'm running now will take about eight 2GHz-weeks, which I can't get to come out to more than about 500 MIPS-years.[/QUOTE]

I was wondering about that 196 myself, before logging on to see whether
you'd replied. I had 73+123, which would seem to be a miscount --- you
might have let us know the p127 to start with (not to mention that the
intended comparison was snfs -- obscure enough that I had to check Scott
Contini's Factor World to refresh my recollection -- and that you'd taken
an average ...). The miscount isn't what was bothering me though; worse,
I neglected to compare snfs difficulties (after objecting elsewhere to using
digits, instead of difficulties --- which is where the runtimes come from).

On the substance, I'm not sure that we ought to be surprized that
leading edge computations are no longer leading edge 8 years later!
Today we ought to be thinking about getting access and then routine
access to lots of processors with 4Gb, not 2Gb. Cf 77-digit prime
(256-bit) ecm factors and factor bases for 768-bit gnfs. -bd

PS -- has data for the 2,772+ stats expired by now? I have a copy of the
relns and guid's (as well as the lattice siever relns, through the last);
but the prospective interest must be decaying rapidly, now that
6, 283- is well along, and as (sounds like) 5,317- may be on the not-
too-far distant horizon.