Thinking out loud about getting under 20M unfactored exponents

[petrw1]

Originally Posted by James Heinrich

There are 350 exponents that are fully-factored (where the last factor is either certainly or probably prime).
All the other exponents (almost?) certainly have factors waiting to be discovered.

Hmmm i expected there would be a lot more.
An extremely low success rate.

Thanks.

[tha]

I am continuing my work in the 15M range for a about a week or so and will then move to the 21M range.

I got the 15M range down from 21480 by 160 now doing P-1.

[LaurV]

Originally Posted by petrw1

As I understand it, (correct me if I'm wrong), once a PRP-(xx??) test is done and verified/certified it can indicate if the remaining factor is a Probable-Prime.
I take this to mean it is a waste of time (or a bigger waste of time) to bother looking for factors of these exponents.
Am I making sense?

You do make sense. There are about 400 exponents for which we know that the mersenne cofactor is PRP. For these, it makes no sense to try splitting the cofactor further, it will be a waste of time. There is an infinitesimal chance the cofactor is pseudoprime (i.e. composite, but behaving as a prime for the most tests we can do), and you may be more famous if you can split such pseudoprime than you can be by finding a mersenne prime, but our "gut feelings" tell us that the cofactor is prime. So, you should not waste time with them. You can find a list of such, on James' page, here.

[masser]

We've now been factoring the 14.0M range for 10 months: 143 factors have been found, with a mix of TF, P-1 and a little bit of ECM. 100 factors to go for the under 2000 goal, so we have passed the halfway point.

It will become harder to find factors, so I'm happy to report that we have gotten some help lately from others on the forum. Many thanks!

VBCurtis, are you still working on the 14.01M subrange? I might restart work there soon, but don't want to step on your toes.

[VBCurtis]

I've paused P-1 for a few weeks to use that core on another project; I plan to start back up mid-month. If you'd like to start at 14.015M, I'll finish 14.010-14.015 for P-1.

I'm still doing ECM on another machine from 14.00M; only at 14001607 today, but I'm doing 10 curves at B1=250k and the server is crediting me with 48 curves per exponent.

[masser]

Originally Posted by VBCurtis

I've paused P-1 for a few weeks to use that core on another project; I plan to start back up mid-month. If you'd like to start at 14.015M, I'll finish 14.010-14.015 for P-1.

Sounds good; I'll use one of my slow gpus to TF 14.015-14.02M from 71 to 72 bits. It's probably the most productive work for that gpu now.

Originally Posted by VBCurtis

I'm still doing ECM on another machine from 14.00M; only at 14001607 today, but I'm doing 10 curves at B1=250k and the server is crediting me with 48 curves per exponent.

I have "finished" working the 14.05M range, too. Most of the remaining candidates there only have 7 t25 curves completed. 14.09M will be "finished" in about a week, also.

[petrw1]

... now that I have your attention

Feb 25 Update:
20 more ranges cleared:
3.2, 4.2, 4.3, 4.5, 6.7, 10.2,
22.9, 23.7, 25.2, 26.1, 29.3, 29.9,
30.1, 32.1, 36.2, 36.5, 37.6, 38.8, 41.7, 43.4

TOTALS to date:
245 total ranges cleared or 49.30% (4 more to half way)
3 Ranges with less than 20 to go.
1,694 more factored (28,739)....52.04% total factored.

My current activity/status:
There are only 6 ranges remaining in 4xM.
- 43.0 is being deep TF'd; it should be done in a couple days.
- I have about 1 more month of deep P-1 to do in 42.6, 48.4 and 49.6.
Then unfortunately these 3 ranges will still have close to 50 left to factor.
I'LL NEED DEEP TF GPU HELP HERE.
- Then for 40.1 and 43.3 I plan to do a little more deep P-1 and try to get them closer to 30 remaining.
That said, if anyone wants to TF them before I get there go for it.

This has me moving into the 3xM ranges early April.
There are only 14 ranges remaining there thanks to some huge help while I was chugging away in 5xM and 4xM.
It appears 38.7 will be cleared via TF.
For the last 13 ranges I plan to spend the rest of 2021 doing deep P-1 to get most ranges to under 20 remaining
(a few closer to 30) at which time TF can complete them.

I've got my GPUs starting to TF 2xM to 73 bits.
I COULD USE HELP HERE.
Several other people are also working in the 2xM ranges; some TF and some P-1

2xM will also require a LOT of DEEP P-1; more than just where B1=B2 currently.
But in these lower ranges P-1 is quite fast and efficient.
I COULD USE HELP HERE TOO.

Thanks again for everyone contributing.

[petrw1]

That is, half of the ranges are cleared.

I started tracking on 2017/07/24 when there were 498 ranges to go.
As of today 249 have been cleared.
The elapsed time is 1,325 days; 3.6 years.

I fully understand that many of these 249 where "low hanging fruit".
But certainly not all; some were very labor intensive ranges too.

This may not mean we are half done as far as time goes.
But then it depends on how much help we get;
and how much faster algorithms or hardware gets.

TF is more efficient for higher ranges; P-1 or ECM for lower ranges.

5xM is complete
4xM has only 4 ranges to go.
3xM has only 13 ranges to go.
2xM has 85.
1xM has close to 100.
0xM has about 50 (all ranges below 3.4M are done)

[VBCurtis]

Originally Posted by petrw1

That is, half of the ranges are cleared.

I started tracking on 2017/07/24 when there were 498 ranges to go.
As of today 299 have been cleared.

Half of 498 is 249. We're well past half the ranges, unless there's a typo in the part I quoted.

[petrw1]

Originally Posted by VBCurtis

Half of 498 is 249. We're well past half the ranges, unless there's a typo in the part I quoted.

Yes, oops 249.

[masser]

Originally Posted by petrw1

I started tracking on 2017/07/24 when there were 498 ranges to go.
As of today 249 have been cleared.
The elapsed time is 1,325 days; 3.6 years.

I think the effort has found over 6000 factors in the past year in the ranges of interest. Have we crossed 30,000 total factors found yet?