20060108, 01:36  #1 
May 2003
7×13×17 Posts 
Finding factors of cunninghamlike numbers
I'm working on a project, and would like to find a table that lists known medium sized factors for numbers with . I found Brent's tables, but they didn't go high enough for me.
For example, I need to find two factors of 13^{862}1 that are >10^{11}. I found one by ECM, and can probably find a second one, but it would be nice to skip all that work if there is a table somewhere. Thanks. 
20060108, 01:47  #2 
Aug 2002
Buenos Aires, Argentina
53A_{16} Posts 
Brent's table cover the range base < 10000, exponent < 10000, but of course most entries do not have enough ECM done. So you can make us a favor by sending to Richard Brent all factors that you find of numbers in this range.
Brent's page is: http://wwwmaths.anu.edu.au/~brent/factors.html. You can find his email there. 
20060108, 02:26  #3 
May 2003
7·13·17 Posts 
Alperton,
As I mentioned in my post, I had found that site, and it didn't (as far as I could find) have the needed factorizations. Further (as far as I could find) it DIDN'T cover the range you said. Rather, just pairs (a,n) for which a^n < 10^255. 
20060108, 03:07  #4  
"William"
May 2003
New Haven
2^{3}×5×59 Posts 
Quote:
William 

20060108, 03:53  #5 
May 2003
7·13·17 Posts 
Right. It gives a few values, but not very many.
Oh well. Maybe I can work around the problem. 
20060108, 04:18  #6  
"William"
May 2003
New Haven
2^{3}×5×59 Posts 
Quote:
Putting this into Alpertron, I get 863 ^ 2 x 68099 x P469 (It hasn't finished the APRTCLE proof as I post this, but it would be an exceptional situation if the proof fails after progressing this far) Are you looking for factors of the algebraic factor 13^4311, or I have I misunderstood something? I don't have much computing power available, but I'll help look for factors of any of p^q1 that you need (p and q odd primes) because OddPerfect.org will eventually be interested in these. William 

20060108, 05:23  #7 
May 2003
7×13×17 Posts 
William,
Thank you. The numbers I am looking at have more to do with odd perfect numbers than you may realize. Give me a couple weeks to settle things down, and I'll send you what I'm working on. Thanks for the factorization in the meantime! That sure is a large prime! 
20060111, 02:14  #8 
May 2003
7×13×17 Posts 
William,
Here is my general question. Consider the equation . All solutions to this, with prime, and prime, are given at http://www.mscs.dal.ca/~joerg/res/fq.html. Write for the multiplicative order of . I'm wondering if it is the case that for those , if is divisible by at least two primes . Also, I'm interested if anyone has searched for solutions to to a higher bound than on that site. Cheers, Pace 
20060111, 03:05  #9 
Jan 2005
2·31 Posts 
If you still need factors of (13^4311)/12, here's what I got:
1605907 * 56586870103 * 16002623839393 * 35910496578500372495225262919339090613 * C412 Presumably you already had the three small ones. Phil 
20060111, 03:18  #10 
May 2003
7·13·17 Posts 
Phil,
Thanks. Actually, William's factor was fine, but yours is good too. It would be nice to have the factors for the other cases, as explained in my last post. Cheers! 
20060111, 03:36  #11  
"William"
May 2003
New Haven
2^{3}·5·59 Posts 
Quote:
Things are a bit mixed up. The site has prime, and prime  a and p reversed from your post. Let's take a specific example and see if I follow. I think that 59 2777 is an example you are interested in. The multiplicative order of 59 mod 2777 is 1388. You want to know if 59^{1388}1 has at least two prime factors > 10^{11}. Or perhaps that isn't enough  it sounds like you want to know the values of two such prime factors  not merely their existence. Is that right? Which ones have already been solved? William Last fiddled with by akruppa on 20060903 at 18:02 Reason: Fixed typesetting tags 

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