20070227, 08:26  #1 
(loop (#_fork))
Feb 2006
Cambridge, England
18EF_{16} Posts 
Head, meet wall
I have just spent about a week trying to factor an aliquotseries number
4002575656069920142792412245296211078849750530528040085185518889509565302305248202324101206943842421375710626210947 by GNFS. All my square roots gave 1*N, I sieved more, rebuilt the matrix, and all my square roots still gave 1*N. This is because 4002575656069920142792412245296211078849750530528040085185518889509565302305248202324101206943842421375710626210947 is in fact a prime number. Well, at least it's not a subtle and hardtotrackdown bug in ggnfs ... 
20070227, 08:52  #2  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2^{3}·11^{3} Posts 
Quote:
Paul 

20070227, 10:21  #3 
"Nancy"
Aug 2002
Alexandria
2,467 Posts 
So does the Aliquot sequence terminate with a prime? What was the starting value?
alex 
20070227, 11:01  #4  
(loop (#_fork))
Feb 2006
Cambridge, England
14357_{8} Posts 
Quote:
I've switched to running gmpecm on the full numbers ... it's not the efficient way to get out factors of 2 or 41, it gets out the small composites in bunches which I have to split with gp, but it does give a primality test after pulling out the small bits. 

20070227, 11:51  #5 
"Nancy"
Aug 2002
Alexandria
100110100011_{2} Posts 
GMPECM has a trial division option: t <limit>
It is quite useful for getting rid of really small factors before actual ECM starts up. It also has a primetest option, which checks inputs for primality, but you have to specify it  there's no such check by default. Alex 
20070305, 07:20  #6 
"Frank <^>"
Dec 2004
CDP Janesville
2×1,061 Posts 
Fivemack,
On the other hand you could do what I do. I start out with a number and put it Dario's ECM applet (http://www.alpertron.com.ar/ECM.HTM). This has the nice feature of taking out all the small primes and any easy ECM factors before I put any remaining composite into my (smallish) ECM cluster. As a bonus, Dario's applet also prime checks the final factorization before pasting the results into the sequence file. And as one more bonus the applet will also perform the sigma calculation, so all I have to do is subtract the previous result right in the applet to start the next step off. I'm currently extending three sequences right now; I might take on a couple more as the numbers get longer. Later, Frank 
20070305, 16:38  #7  
Oct 2006
vomit_frame_pointer
168_{16} Posts 
Quote:
Quote:


20070305, 18:15  #8  
∂^{2}ω=0
Sep 2002
Repรบblica de California
2·5,813 Posts 
Quote:
(NFS program authors take not as well.) This will also catch any occurrences of composites due to potential other reasons, e.g. candidateprocessing scripts in some kind of automated factoring flow, data corruption in a networked effort, etc. Sure, it's not unreasonable to assume users of such code will do such a test themselves, but like I said if the functionality is already there or is trivial to add... 

20070305, 18:55  #9  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
10100110011000_{2} Posts 
Quote:
Paul 

20070306, 08:22  #10 
"Nancy"
Aug 2002
Alexandria
2,467 Posts 
Ernst,
the problem is that with large input numbers that are to be tried with low B1 values, doing a PRP test first will take several times the time of the P1/ECM/whatever attempt. We'd need some threshold for which numbers get a PRP test and which ones don't. So far, we'd simply taken 0 as that threshold... Alex 
20070306, 12:07  #11 
Jul 2005
2·193 Posts 
I agree, in my hacked version of ecmnet I test for primality when adding the number to the server, not before each and every curve.
It may be ok if you're making ecm do multiple curves on the same number, but the way my ecmnet works is that each client does one curve and then reports back. A primality test each time would soon add up, especially as the server has had several million curves returned. 
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