20210816, 01:18  #1 
Mar 2019
USA
3·23 Posts 
Factor Found P1 Question
I don't find many factors using P1, but when I do I always find it interesting. I have a question when looking at the results:
See: https://www.mersenne.ca/exponent/107731187 In the "P1 results:" section, where it says "bits (76.408)", does this mean that if someone had simply TF'ed it from 7677 that it would have found that same factor? 
20210816, 01:52  #2 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
2·5,059 Posts 
That is correct.

20210816, 02:27  #3 
"University student"
May 2021
Beijing, China
2·3^{2}·7 Posts 
I've even found a factor like this.
M107599963 has a factor: 118142113851371427649409 (76.645 bits) k: 2^6 × 83 × 179 × 13187 × 43783 I TFed to find this one, but it's really P1smooth 
20210816, 02:58  #4 
Mar 2019
USA
1000101_{2} Posts 
Thanks...because when I look at one like this:
https://www.mersenne.ca/exponent/107934373 And I see bits is 122.960, I think "Damn, that would take a LONG time to TF". 
20210816, 04:47  #5 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
5,923 Posts 
It takes quite a lot of P1 to get one or more in the top 100 (>131.75 bits) of https://www.mersenne.ca/userfactors/pm1/1/bits

20210816, 22:25  #6  
Jul 2003
Behind BB
3·587 Posts 
Quote:


20210817, 02:12  #7 
Romulan Interpreter
"name field"
Jun 2011
Thailand
2650_{16} Posts 
Indeed. All x.zzzz bits factors found by P1 will be found also by TF, if you TF from x to x+1 bits.
However, viceversa is not true. If you find a factor by TF from x to x+1 bits, this factors will be found by suitable P1 to some B1/B2 limit, only if the factors is B1/B2 smooth. TF finds all factors between x and x+1 bits (unless you stop after the first factor found, obviously). P1 finds only "smooth" factors, regardless of their "bit" size. So, the two methods have a nonvoid intersection, and a nonvoid nonintersection (i.e. there exist factors that will be found by both methods, and there exists factors that are very easy to find by one method, but closetoimpossible to find with the other  otherwise we won't use both methods here). Last fiddled with by LaurV on 20210817 at 02:17 
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