[QUOTE=frmky;114889]First, check to see if it has any useful factorizations. In this case, it doesn't. It simply factors as (9^4 + 8^4)*(something big and not useful).

Write it as 3^344 + 2^516. For this size, I've had good success with 5th order polynomials. Multiply the above by 3, and it can be written as 3^345 + 6 * 2^515. Divide this by 2^515, and it becomes (3^69 / 2^103)^5 + 6. So your algebraic polynomial is x^5 + 6. The linear poly must have the same root (mod n), so use the simple one, x - 3^69 / 2^103. Multiply this by 2^103 and you have your linear poly: 2^103 x - 3^69.

So, barring any simple mathematical errors on my part, your polys are
x^5 + 6 and
2^103 x - 3^69

As far as parameters for numbers of this size, I've had good success with factor base limits of about 10.5 million on each side, large prime bounds of 2^28 on each side, and mfbr/a of 52 bits. For the skew, I use (c0/c5)^(1/5), or about 1.4 in this case. I collect the unprocessed relations from the GGNFS lattice siever and use msieve for the postprocessing. I estimate that it will require about 16 - 17 million relations (1.7 - 1.8 GB in storage space) with these parameters to complete the factorization, and will take 1-2 weeks on a single modern pc.

Greg[/QUOTE]


Greg, thank you for the explanation but I think my machine will not be able to handle this kind of big factorization :sad:

[QUOTE=CedricVonck;114898]Greg, thank you for the explanation but I think my machine will not be able to handle this kind of big factorization :sad:[/QUOTE]


Why? I can do it in about 2 weeks on a single 1.5GHz PC with only 512Mbytes
of memory. This factorization is not large by current standards.

Because my pc is only turned on for about 12 hours a day?
And this particular machine has a heat throttle on the cpu.
The sound is really overpowering when trying to sleep.

I will see how far I will get

[QUOTE=CedricVonck;114966]Because my pc is only turned on for about 12 hours a day?
And this particular machine has a heat throttle on the cpu.
The sound is really overpowering when trying to sleep.

I will see how far I will get[/QUOTE]

The machine running only half-time simply means that it will take twice
as long...

Anotehr update
 

I've just posted another update to the tables at [url]http://www.leyland.vispa.com/numth/factorization/anbn/main.htm[/url]

Fourteen more numbers have been completely factored, leaving 78 still to be done. As soon as another 28 have been completed I'll extend the tables again. The ECMNET server has not yet been brought up to date with regard to these new factors. I''ll do that work shortly.

All the factors this time have come from Chad Davis and Bob Silverman.

Paul

[QUOTE=xilman;118224]I've just posted another update to the tables at [url]http://www.leyland.vispa.com/numth/factorization/anbn/main.htm[/url]

Fourteen more numbers have been completely factored, leaving 78 still to be done. As soon as another 28 have been completed I'll extend the tables again. The ECMNET server has not yet been brought up to date with regard to these new factors. I''ll do that work shortly.

All the factors this time have come from Chad Davis and Bob Silverman.

Paul[/QUOTE]

78 to be done? The [URL="http://www.chiark.greenend.org.uk/ucgi/~twomack/homcun.pl"]reservation page[/URL] says that there are "only" 69 to be done.

[QUOTE=Andi47;118234]78 to be done? The [URL="http://www.chiark.greenend.org.uk/ucgi/~twomack/homcun.pl"]reservation page[/URL] says that there are "only" 69 to be done.[/QUOTE]Look carefully.

There are 69 waiting to be reserved and 9 reserved. Last time I checked, 69+9 = 78 (in decimal arithmetic, anyway).


Paul

Another update
 

Another update to the tables has just been uploaded.

There are 52 composites remaining in these tables, so extensions to some of them will be added shortly.

Over the last couple of months I've found a few thousand small factors from the extensions, and several dozen relatively large ones. Chad Davis has also helped enormously by factoring dozens of numbers in the C70-C100 range by mpqs. Thanks Chad!


Paul

The number of remaining composites has dropped to 50.

How much ECM has been done on the remaining ones?

Extension tables just loaded.
 

I've extended the base 10, 11 and 12 tables and loaded the 589 remaining composites into the ECMNET server run by Phil Carmody at 83.143.57.194:8194. The old tables at that server have now been retired from the ECMNET server, though are still available for GNFS factorizations.

My web page at http:[url]www.leyland.vispa.com/numth/factorization/anbn/main.htm[/url] has been updated similarly.

A few small composites suitable for MPQS are available; to find them you'll have to download my tables :smile: These composites appeared from ECMNET factorizations which ran after Chad's sterling work in clearing out those under 100 digits.

I'll be liasing with Tom Womack shortly, so he can update his reservation system if he wishes.


Paul

Via ecm:

[code]
[2007-12-28 19:44:03 GMT] Factor found! 11+2_169 / 4670162227798161653429464151273 B1: 1000000 sigma: 498317136 Type: probable Cofactor is 'Probable': 198664862651776280084877059003248365711846661384561520265135284192526152494950343 (found in step 2)
[/code]

Will do the cofactor by ggnfs