20070810, 07:29  #1 
Apr 2007
44_{8} Posts 
The factorization of primorials +/ 1
Hi all,
As a hobby project I extended the tables for the primorials +/ 1 from the World Integer Factorization Center. Right now I have the tables with n <= 160. I did quite some amount of ECM work on the extensions as well as one the original tables (and managed to find quite some prime factors). I have mailed Hisanori Mishima but not all my new factors for the original list are on the WIFC website yet. If anyone is interested in helping out please report ECM work done or factors found in this thread. I made a very basic website showing how many curves I have done on these numbers together with the tables at primorial.unit82.com. Furthermore I am quite interested in any theory about the factorization of these numbers. When searching for some articles I managed to find only a few about the primorial primes, so if anyone knows some good resources please let me know! Thanks, Joppe 
20070811, 02:14  #2 
"Jason Goatcher"
Mar 2005
5×701 Posts 
I'm reserving 76#+1 here (Edit: and 82#+1), since I figure this is the most obvious place. If someone wants to give me editing privileges, I'll restrict myself to this thread and only handle the tracking.(I would suck as a mod, but I'm sure people already know that)
Last fiddled with by jasong on 20070811 at 02:25 
20070811, 02:32  #3 
"Jason Goatcher"
Mar 2005
5×701 Posts 
If I may ask a stupid question. How do you put comments in an ecm input file?

20070811, 02:42  #4 
Jun 2003
3045_{8} Posts 
I have always wondered about this, but never had the time to implement this...
If we take P#+1 or P#1 and do a P1/P+1 test using B1=P, how many factors would be end up finding? What would be the distribution of such factors? Are any such factors known for large P? 
20070811, 04:35  #5 
Jun 2003
11^{2}×13 Posts 
The only solution I know of is 2#+1 is divisible by 3. Are there any more?

20070811, 10:15  #6  
Apr 2007
44_{8} Posts 
Quote:
Lines beginning with a "#" are comments as far as I know. Last fiddled with by Joppe_Bos on 20070811 at 10:17 Reason: Typo 

20070811, 11:14  #7  
Apr 2007
2^{2}·3^{2} Posts 
Quote:
Quote:
About the nontrivial factors I have no idea about the distribution (interesting question!), the first nontrivial factor which can be found with Pollard p1 with pound p_n is when n = 7 so p_7# + 1 = 17# + 1 = 510511 which has a factor 2 * 3^2 + 1. 

20070811, 12:15  #8 
"Mark"
Apr 2003
Between here and the
2·2,963 Posts 
Set up an ECMNet server and you will probably have many more helpers.

20070811, 18:55  #9  
Jun 2003
11^{2}×13 Posts 
Quote:
In short find n such that P#+1== 0 (mod n) and the largest prime divisor of n1 is smaller or equal to P. I tested all n up to 100K, but did not not find a solution except n=3. Similarly, find x such that P#1==0 (mod x) and the largest prime divisor of x+1 is smaller or equal to P. No solutions for this. 

20070811, 20:18  #10  
Jun 2003
11^{2}×13 Posts 
Quote:


20070811, 23:17  #11 
"Jason Goatcher"
Mar 2005
5·701 Posts 

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