20181201, 14:06  #1 
Random Account
Aug 2009
19·101 Posts 
ECM B1 vs B2
I have been studying the ECM Progress page on mersenne.org off and on for several days. As it goes across, the B1 values get really large, rapidly. Running some of these high values could be really time consuming, considering B2 = B1 * 100.
I do not understand why B1 must be so large in these cases. Here is my question: What happens in B1 that does not happen in B2, and viceversa? Thank you. 
20181201, 15:26  #2 
Sep 2002
Vienna, Austria
3×73 Posts 
The main difference is that the ECM group order can have many prime factors below B1, and only one between B1 and B2.

20181201, 15:30  #3 
"Victor de Hollander"
Aug 2011
the Netherlands
2^{3}×3×7^{2} Posts 
Short answer:
You need larger B1&B2 values to find larger factors. 
20181201, 15:49  #4 
Random Account
Aug 2009
19×101 Posts 

20181201, 19:41  #5  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2×5,323 Posts 
Quote:
The complete answer is left as an exercise. You should learn at least a little about the ECM (and the P1 method from which it was developed) before asking questions like these, not afterwards. 

20181201, 23:50  #6 
Random Account
Aug 2009
11101111111_{2} Posts 
I should have known better than to ask. I am not a mathematician. I looked at Wiki results before asking. All the formulas shown there, I do not understand. At my age, it is too late to start. End of story.

20181202, 00:59  #7 
"Victor de Hollander"
Aug 2011
the Netherlands
2^{3}·3·7^{2} Posts 

20181202, 02:00  #8 
Random Account
Aug 2009
3577_{8} Posts 

20181202, 02:56  #9  
Aug 2006
13541_{8} Posts 
Quote:
You could easily set up a method with just a B1 that looked for numbers with all its prime (power) divisors smaller than B1. But then you might have to make B1 large, and that's hard. As a compromise, you can design the method in a different way: instead of all the primes needing to be smaller than B1, you can have one exception which is bigger than B1. But it still has to be smaller than B2. So running B1 = x, B2 = y is a way to avoid running the first method with just B1 = y. Does that make sense? Last fiddled with by CRGreathouse on 20181202 at 02:57 

20181202, 04:47  #10  
"Curtis"
Feb 2005
Riverside, CA
3×1,579 Posts 
Quote:
Roughly speaking, we could search with B1 = 2M, allowing any number of factors less than 2M; or, for a similar amount of time, we can search to B1 = 1M and B2 = 100M, which allows any number of factors below 1M *and* one between 1M and 100M. The latter case covers more situations than the former, so we use Stage 2 and a B2. 

20181205, 15:20  #11  
Random Account
Aug 2009
19×101 Posts 
Quote:
During my studying, I matched B1 and B2. This became cumbersome rapidly. I also experimented with B2 = B1 * 10. This didn't really cover the ground it needed to. Quote:
I want to emphasize that all of this was for a leaning experience, only. What the server gives me, I run as is. Thank you all for your time. Most kind. 
