20190402, 12:39  #12  
Feb 2017
Nowhere
2^{2}·7·109 Posts 
Quote:
Quote:
So the reason for wanting these factorizations is clear enough. I'm sure having at least one of the smaller remaining composites ECM'ed beyond current limits would be appreciated. 

20190402, 14:30  #13 
Jul 2018
34_{8} Posts 
At risk of being the 5yearold with the "why"s, I want to know why the poster wants to know that that number is prime...

20190402, 15:06  #14  
Feb 2017
Nowhere
101111101100_{2} Posts 
Quote:
There are, of course, methods for proving N prime other than those involving the factorization of N  1 or N + 1. It is possible that one or more of them might be better suited to the purpose that the factorization approach. In the almost yearold thread, and in subsequent threads, it has been pointed out that the remaining composites are much larger than composites on "mostwanted" lists. This one is for remaining factors of Cunningham numbers. The "most wanted" is 2^1207  1, a C337. 

20190402, 15:11  #15  
"Luke Richards"
Jan 2018
Birmingham, UK
117_{16} Posts 
Quote:
So this PRP is one I discovered in March 2018. I'm a high school teacher so in order to induce some interest in primes among my classes I had all 240568 digits printed on a huge poster and put up in my classroom. It's great, the kids love it. Every now and again a kid takes a real interest in primes and goes away and looks into them, coming back having found out that large primes are very hard to prove and asks if I've proved it. I always say 'no', but some kids ask me how I'm doing with proving it. Obviously the answer is usually 'not very far' but I like to have something to explain what I'm doing to try. Saying "it's practically impossible, I've pretty much given up" doesn't give the kind of message to the kids I want to give them about not giving up etc. (I'm sure others will argue that I should be teaching kids to be realistic about their goals etc, which I do agree with but it's a nuance that would be lost on teenagers. They would just hear 'i've given up' which I don't believe is a great message to give them. 

20190402, 17:15  #16  
Sep 2003
2·1,289 Posts 
Quote:
The C1996 is (3^4462+1)*10/(3^194+1)/(3^46+1)/135641573315088856753 Surely (3^4462+1) hasn't been ECM'd to anywhere near t=60. I was finding numerous factors for 3+ with prime exponents in low ranges as recently as a few months ago with a mere t=25. Just one example, the 28digit factor 3,1637,+,4426039274041115597684571331 was unknown to FactorDB before December of last year and was also unknown to the Brent tables (myfactors.mooo.com). Not sure who found that one, it wasn't me. 

20190402, 20:41  #17 
"Curtis"
Feb 2005
Riverside, CA
4,001 Posts 
I suspect penlu conflated "find a factor" with "fully factor". The usual heuristic of a 1/n chance to find an ndigit factor should still apply; the catch is that the cofactor is highly likely to be composite, so finding a factor in the 40 to 60 digit range with ECM, while cool, is highly unlikely to help one along the way to "fully factored". No idea where penlu got the 1/10^85ish chance, though; a single newfound factor has a higher chance than that to result in a prime cofactor!

20190402, 21:59  #18  
Sep 2003
2·1,289 Posts 
Quote:
If you actually won, it would be due to sheer incredible luck and not hard work or perseverance. And that would still be true even if you'd been diligently spending £100 on lottery tickets every week without fail for your entire life. So how does that send a positive message? The lottery analogy breaks down somewhat because technological advances will steadily improve the odds over time, as others have pointed out. But probably not enough to make a difference in your lifetime, unless you make a fortune and spend it all on your deathbed. 

20190403, 04:38  #19  
Jul 2018
2^{2}×7 Posts 
Quote:
Last fiddled with by penlu on 20190403 at 04:39 

20190403, 07:34  #20  
"Luke Richards"
Jan 2018
Birmingham, UK
3^{2}·31 Posts 
Quote:
I do completely get what you are saying though  there's a message about being realistic about our challenges, setting achievable goals which is also important. However, it's important to realise and appreciate that as a high school teacher the biggest challenge we often face is "this is difficult, I give up" and I'm modelling the behaviour I want to see from them. 

20190403, 08:33  #21 
Mar 2018
3·43 Posts 
I, for one, approve your stance and desire to prove this number no matter how futile and improbable that is. Though I don't really like kids, this not giving up example is important for a teacher.
But yeah, as others said, helping the Cunningham project doesn't directly or even indirectly help unless you're working with ECM on specific remaining cofactors (C1996, C2329, C10253 and maybe C225698 too from 3^504206+1 and C3664, C14795, C44395 and maybe C177595 too from 3^504205+1), which Cunningham project currently doesn't and wouldn't for probably a long time. This reply in another thread was a good outline of chances and directions for the hobby project future. 
20190403, 13:08  #22 
Feb 2017
Nowhere
101111101100_{2} Posts 
Just by way of "not giving up," It occurred to me to wonder if you had checked, for your PRP number N = 3^504206 + 2, and some base b,
gcd(N, Mod(b,N)^((N1)/f)  1), and f = each known prime factor of 3^504206 + 1 and also (just for the sake of thoroughness) f = each composite cofactor with no known proper factors. 
Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Cunningham ECM efforts  pinhodecarlos  Cunningham Tables  7  20171221 13:29 
Cunningham ECM Now Futile?  R.D. Silverman  GMPECM  4  20120425 02:45 
Cunningham Project on YouTube  Batalov  Cunningham Tables  0  20120226 02:58 
Extended Cunningham or so  rekcahx  Factoring  6  20110819 12:45 
Introduction: ECM work done on Cunningham Project composites  garo  Cunningham Tables  2  20050120 10:06 