Exponent Progression
 

The exponent testing process beyond TF has always been a bit muddy to me. Specifically, the existence of P-1 [U]and[/U] ECM. So, I'll put some progressions below and someone tell me which applies.

1. TF .. P-1 .. LL .. DC
2. TF.. ECM .. LL .. DC
3. TF .. P-1 .. ECM .. LL .. DC
4. TF .. ECM .. P-1 .. LL .. DC

Thanks! :smile:

[QUOTE=storm5510;457196]The exponent testing process beyond TF has always been a bit muddy to me. Specifically, the existence of P-1 [U]and[/U] ECM. So, I'll put some progressions below and someone tell me which applies.

1. TF .. P-1 .. LL .. DC
2. TF.. ECM .. LL .. DC
3. TF .. P-1 .. ECM .. LL .. DC
4. TF .. ECM .. P-1 .. LL .. DC

Thanks! :smile:[/QUOTE]

[url]https://www.mersenne.org/various/math.php[/url] isn't clear enough ?

[QUOTE=storm5510;457196]1. TF .. P-1 .. LL .. DC
[/QUOTE]

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.

[QUOTE=ATH;457205]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.[/QUOTE]

Correct. But ECM is the only way to look for factors of Fermat numbers below F30... :smile:

[QUOTE=ET_;457207]Correct. But ECM is the only way to look for factors of Fermat numbers below F30... :smile:[/QUOTE]

Yes, that is another use of ECM. But that is still not GIMPS main project, so not relevant to OPs question about "exponent progression".

[QUOTE=ATH;457205]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.[/QUOTE]

I'm running P-1's now, so I was on the right track. I looked through the reports on the GIMPS site and noticed the ECM exponents were quite small.

One question answered and one curiosity solved. Thank you very much. :smile:

It actually depends on your machine. The right path may be TF, P-1, [B]TF[/B], LL. Considering that sometimes is more efficient to do P-1 before last(s) bits of TF, especially for very large exponents.

[QUOTE=LaurV;457284]It actually depends on your machine. The right path may be TF, P-1, [B]TF[/B], LL. Considering that sometimes is more efficient to do P-1 before last(s) bits of TF, especially for very large exponents.[/QUOTE]

TF after P-1. I take it that a very large exponent would be one needing factored beyond 75 bits? The P-1 assignments I receive are factored to 2[SUP]75[/SUP] and are in the 81-million range. I've done a few TF's to 2[SUP]75[/SUP] with [I]mfaktc[/I] and it's a bit tedious on this hardware.

I'm running a DC with [I]CuLu[/I] that was factored to 2[SUP]72[/SUP]. The exponent is in the 45-million range. According to the table in the 'Math' page, this is right on.

Thanks! :smile:

I think the P-1 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.

[QUOTE=ATH;457467]I think the P-1 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.[/QUOTE]

Part of it is a balancing game between how fast the GPU wokers can TF versus how quickly the P-1 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.

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 former-last, for about the same chance to find a factor (1/n vs. 1/(n+1), or so, see GIMPS math page). For P-1 the chances get higher faster, with the amount of work you do (limits, FFT size). Therfore the P-1 and TF "chances curves" will still intersect somewhere, and unless that is exactly in an integer point, it will still be advantageous to do P-1 before last bit of TF for some ranges. Especially thinking that we also use GPUs to do P-1 too (see cudaPM1).