[QUOTE=R.D. Silverman;112592]Here are a few lines from the table at:


[url]http://www.leyland.vispa.com/numth/factorization/anbn/9+8.txt[/url]

135 P69
136 1862583595234721.27577451610480123780025759297. P79
137 13303523.5814743609.89534726097264584137.202629831798581235224170114127947674113633. P52
138 277.6738541.3956998753.268392054481.38073249796033.1083142670013493. P26
139 1950449.64973847674507. C112
140 9521.104586721.9722288339825561675068321. P55
141 283.113535739.26828459910941672000233146121. P49


The entry for 139 lists a C112. Yet this number has not appeared in
any of the update files, nor is it on the reservations list (that I can find)[/QUOTE]



The entry for 9,7,143+ also seems to be missing... I have this number
fully factored in my tables. There may be other missing numbers as well.

[QUOTE=R.D. Silverman;112593]The entry for 9,7,143+ also seems to be missing... I have this number
fully factored in my tables. There may be other missing numbers as well.[/QUOTE]
It's a C111 in my tables.

Please mail me your factorization and I'll add it to my tables.

I'm surprised that my automagic garnering of factors hasn't picked up everything you've sent in the past, assuming you sent me that one.


I'll mail you all the numbers I believe still to be composite so we can cross-check our tables.


Paul

[QUOTE=xilman;112596]It's a C111 in my tables.

Please mail me your factorization and I'll add it to my tables.

I'm surprised that my automagic garnering of factors hasn't picked up everything you've sent in the past, assuming you sent me that one.


I'll mail you all the numbers I believe still to be composite so we can cross-check our tables.


Paul[/QUOTE]


Here it is:
143 (1,11,13) 27743.168948085557588181063736255986214131378011799.1109910752374095425380960456788063151940546543335015031533214617913

In the log file from my reservations server, I have a note that at 11:01:32BST on 26th July, somebody submitted the factor 168948085557588181063736255986214131378011799 for 9^143+7^143 which was reserved by Bob Silverman.

7,5,205-.c119 factored.

[CODE]
Number: 7_5_205M
N=54814708436245992442100810834915713343640736362611433416566101102748762581073923891414781395443838716086492479426441511
( 119 digits)
SNFS difficulty: 138 digits.
Divisors found:
r1=9873294020445605937884222927707767247696587114238136245061 (pp58)
r2=5551815667874952073437499971611223228873637274238861674179451 (pp61)
[/CODE]

Tables updated
 

The web page has just been updated. The ECMNET server has also been tidied up to remove the factorizations noted since the last update.

There are now 105 remaining composites. As before, when this number falls below 50 I'll add some extensions to the tables.


Paul

Can anyone please show me how to construct a polynominal for this number?

((9^172)+(8^172))/(805864266927076489926257529007561143841)
= C122

The degree should be 5 or should it be of the 6th degree.

For the rest of parameters, I really do not know.

I am always prepared to learn ... and to listen to someone who explains it to me in a calm, and constructive way.

Thank you

[QUOTE=CedricVonck;114878]Can anyone please show me how to construct a polynominal for this number?

((9^172)+(8^172))/(805864266927076489926257529007561143841)
= C122

The degree should be 5 or should it be of the 6th degree.
[/QUOTE]
If the objective is to finish the factorization quickly, it probably would be just as fast to run GNFS on the C122 as it would be to run NFS with polynomials assuming a C164.

Jason,

It is not the meaning that I complete it quickly.
It is the objective that I learn something.

I dont have the necessary resources to do a GNFS of this "magnitude".

[QUOTE=CedricVonck;114881]
I dont have the necessary resources to do a GNFS of this "magnitude".[/QUOTE]
You have the option of running GNFS on a 122-digit composite (~1 machine week on a modern CPU) or SNFS on the 164-digit complete number (~1 machine week, based on the time people need for XYYXF factorizations). Those are pretty much the only choices. I don't think I can help you on finding SNFS polynomials though.

[QUOTE=CedricVonck;114878]Can anyone please show me how to construct a polynominal for this number?

((9^172)+(8^172))/(805864266927076489926257529007561143841)
= C122

The degree should be 5 or should it be of the 6th degree.

For the rest of parameters, I really do not know.

I am always prepared to learn ... and to listen to someone who explains it to me in a calm, and constructive way.

Thank you[/QUOTE]

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