20170421, 16:03  #1 
Random Account
Aug 2009
7^{2}×41 Posts 
Exponent Progression
The exponent testing process beyond TF has always been a bit muddy to me. Specifically, the existence of P1 and ECM. So, I'll put some progressions below and someone tell me which applies.
1. TF .. P1 .. LL .. DC 2. TF.. ECM .. LL .. DC 3. TF .. P1 .. ECM .. LL .. DC 4. TF .. ECM .. P1 .. LL .. DC Thanks! 
20170421, 16:30  #2  
"Forget I exist"
Jul 2009
Dumbassville
20C0_{16} Posts 
Quote:


20170421, 17:06  #3 
Einyen
Dec 2003
Denmark
3·5·7·31 Posts 
ECM is only used on smaller exponents below the LL and DC range for people to find more factors of already factored or DC'ed exponents.
ECM was never used in GIMPS main project. It is too slow and combined with the low chance of finding a factor, it is faster on average to run the LL test. 
20170421, 17:35  #4  
Banned
"Luigi"
Aug 2002
Team Italia
2×41×59 Posts 
Quote:


20170421, 22:58  #5 
Einyen
Dec 2003
Denmark
3·5·7·31 Posts 

20170422, 03:52  #6  
Random Account
Aug 2009
7^{2}·41 Posts 
Quote:
One question answered and one curiosity solved. Thank you very much. 

20170422, 17:39  #7 
Romulan Interpreter
"name field"
Jun 2011
Thailand
10011010001110_{2} Posts 
It actually depends on your machine. The right path may be TF, P1, TF, LL. Considering that sometimes is more efficient to do P1 before last(s) bits of TF, especially for very large exponents.

20170425, 02:05  #8  
Random Account
Aug 2009
7^{2}×41 Posts 
Quote:
I'm running a DC with CuLu that was factored to 2^{72}. The exponent is in the 45million range. According to the table in the 'Math' page, this is right on. Thanks! 

20170425, 11:03  #9 
Einyen
Dec 2003
Denmark
CB7_{16} Posts 
I think the P1 test before the last bit of TF was something that was done back before GPU took over most of the TF, I don't think that is done anymore, but not completely sure.

20170425, 13:11  #10 
"/X\(‘‘)/X\"
Jan 2013
2937_{10} Posts 
Part of it is a balancing game between how fast the GPU wokers can TF versus how quickly the P1 workers will complete a higher TF'ed exponent. Ideally the TF is done first to fully utilize the available GPU power to save the CPU power.

20170425, 15:41  #11 
Romulan Interpreter
"name field"
Jun 2011
Thailand
2·3·5·7·47 Posts 
It doesn't matter what machines you use, and how fast is one compared with the other. If GPUs become 1000 times faster than they currently are, we will raise the factoring bitlevel with a couple of bits (ten, more exactly, as the amount of work doubles with each bitlevel), but it will still be that the last bitlevel takes a double amount of time than the formerlast, for about the same chance to find a factor (1/n vs. 1/(n+1), or so, see GIMPS math page). For P1 the chances get higher faster, with the amount of work you do (limits, FFT size). Therfore the P1 and TF "chances curves" will still intersect somewhere, and unless that is exactly in an integer point, it will still be advantageous to do P1 before last bit of TF for some ranges. Especially thinking that we also use GPUs to do P1 too (see cudaPM1).
Last fiddled with by LaurV on 20170425 at 15:44 
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