How to read the "Exponent Status Distribution"

[3mg4]

Hello again, and sorry for another beginner question.

When i look up the "Exponent status Distribution" list under http://www.mersenne.org/primenet/

I see the list of all work types and how many are left of each kind, i assume i need to read the table from right to left, see attachment, a work type is done when the column Available is empty.
Correct?

The table "PrimeNet ECM Progress" under http://www.mersenne.org/report_ecm/
shows me the same only for ECM?

Example:
So when i have checked the option i only wanna have the smallest possible assigned and forced the Work type to ECM, I should get ECM between 0 and 1.000.000 regarding the attached photo.

Maybe this is all in the wiki, I dont think so or I dont know how to search it. Feel free to post a useful link.

English is not my native language, I apologize for any Grammar and spelling mistakes and promise I will get better!

Thank you for your answers
Gabriel aka 3mg4

[NBtarheel_33]

Originally Posted by 3mg4

Hello again, and sorry for another beginner question.

No problem at all. Every question (and answer) adds to the archive of GIMPS help, information, and answers that this forum will offer for years to come.

Originally Posted by 3mg4

When i look up the "Exponent status Distribution" list under http://www.mersenne.org/primenet/

I see the list of all work types and how many are left of each kind, i assume i need to read the table from right to left, see attachment, a work type is done when the column Available is empty.
Correct?

First of all, unfortunately, I am not seeing any attachment to your post. But let's pull up the Exponent Status Report and walk through the labels just under the header "Exponent Status Distribution":

• Exponent Start - this is simply the start of each range (note that each range has length one million (1,000,000)).
• Range Count - this is the number of prime exponents (i.e. the number of candidates) in a given range. For example, you will note that the 12M range has 61,192 candidates. This is because there are 61,192 prime integers between 12,000,000 and 12,999,999.
• P - this is the number of Mersenne primes (if any) that have been discovered in each range. Note that the lion's share (33) of the 49 known Mersenne primes are in the first range, I.e. between 2 and 999,999.
• Continuing to the right, you will next see the label "Composite" with the sub-labels F and LL-D. For each range, these are the numbers of candidates within the range for which (at least) one factor has been found (the F label) or for which both a first-time and a matching double-check LL test have been performed (LL-D meaning LL-Double-Checked). You will note that in all of the ranges below 35M, every candidate has either been factored or double-checked. Thus, for every range below 35M, you will see that the numbers under F and LL-D should sum to the Range Count.
• Moving again to the right, you see the label "Status Unproven" with the sub-labels LL, LLERR, and NO-LL.
  • LL is the number of candidates within the range that have been LL-tested at least once (note that a candidate may be tested more than once, but still not be eligible for the LL-D column, because none of the test results agree).
  • LLERR is the number of candidates within the range that have been LL-tested but the test was returned with a non-zero error code (indicating that errors occurred during the test). Note that a non-zero error code does not necessarily mean a result is bad, nor does a zero error code mean that a test is always good. About 1-2% of the time, a test will finish with a zero error code, only for a later double-check to show the test result is nevertheless incorrect.
  • Finally, NO-LL is the number of exponents in the range that are yet to be LL-tested (in a sense, the "virginal" exponents).
  • Note that the sum of the "Status Unproven" columns, the "Composite" columns, and the "P" column should be equal to the "Range Count" for each range.
• Next comes the "Assigned" label with its five sub-labels: ECM (below 20M), TF (above 20M), P-1, LL, and LL-D.
  • ECM is the Elliptic Curve Method of factorization, which is attempted (and is only computationally feasible) on candidates below 20M or so. TF is the traditional trial factoring that is performed to an appropriate bit level on candidates larger than 20M. P-1 factoring is another method of factorization that can sometimes find much larger factors that would not ordinarily be found in the course of regular trial factoring.
  • As you might by now guess, the sub-labels ECM, TF, P-1, LL, and LL-D under the "Assigned" label are indicating the numbers of candidates in each range that have been "checked out" by GIMPS users for such tests.
  • Note that there will be overlap between these columns: an exponent may be simultaneously undergoing factoring and LL testing, factoring and double-checking, or even LL testing and double-checking, assigned to different users for such (and hence the same assignment being counted twice (or more) in different columns).
• Finally, there is the "Available" label with the same five sub-labels as the "Assigned" label. These columns give the number of candidates in each range that are available for assignment as ECM, TF, P-1, LL, or LL-D. A typical candidate will start out as TF, then move to P-1, then back briefly to TF, then on to LL, and eventually LL-D. This reflects the steps in processing a candidate exponent: trial factoring, P-1 factoring, the final bit of trial factoring, the LL test, and then the LL double-check.

Originally Posted by 3mg4

Example:
So when i have checked the option i only wanna have the smallest possible assigned and forced the Work type to ECM, I should get ECM between 0 and 1.000.000 regarding the attached photo.

Again, I am not seeing the "attached photo", but yes, the smallest possible ECM assignments are in the range 2-999,999. In fact, there are 16,522 available such assignments right now.

Please post a follow-up if there is anything else that we may clear up for you.

[3mg4]

Thank you, and yes i forgot the pictures,every thing is clear now.
Thank you!

[AlexCara]

First of all I apologize for my ugly english.
I'm a new forum's user at this moment just out of curiosity.
I red your post about the Exponent Status Report. Very clean explanation.
But.... I am searching for the status of each exponent.
May you help me?

[Uncwilly]

Originally Posted by AlexCara

But.... I am searching for the status of each exponent.

Have you found this link ( http://www.mersenne.org/report_exponent/ )? From the PrimeNet page Reports-> Detailed Reports -> Exponent Status

[AlexCara]

My dreams come true. Tnks a lot!

[jwnutter]

Great, explanation Nathan. This is exactly the information I was looking for.

That said, I do have a few follow up questions for you if you don't mind.

For example, you will note that the 12M range has 61,192 candidates. This is because there are 61,192 prime integers between 12,000,000 and 12,999,999.

In regards to the 61,192 candidates in the 12M range. Why is this the case and how is this number determined?

This reflects the steps in processing a candidate exponent: trial factoring, P-1 factoring, the final bit of trial factoring, the LL test, and then the LL double-check.

Lastly, why does a candidate go from TF to P-1 and then back to TF exactly? More specifically, what is the purpose of the second TF step? What prevented the first TF step from completing the process. My apologies if this is covered in the TF and P-1 links you provided. I haven't read these posts yet, but they're next on my list to investigate further.

Thanks in advance for the additional details. And thanks again for this excellent summary of the Exponent Status Report.

[Uncwilly]

Originally Posted by jwnutter

In regards to the 61,192 candidates in the 12M range. Why is this the case and how is this number determined?

That is just the number of prime numbers between those numbers. Any Mersenne Prime must have the exponent (the p in 2^p-1) that is prime. Anyone of hundreds of prime list generating programs will work to make that list. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, etc.

Lastly, why does a candidate go from TF to P-1 and then back to TF exactly? More specifically, what is the purpose of the second TF step? What prevented the first TF step from completing the process. My apologies if this is covered in the TF and P-1 links you provided.

That is a benefit vs. effort issue. P-1 can overlap with TF a little bit in the factors that it finds. We have in the past gained a little extra total system throughput by doing it this way (each step of TF is twice the work of the previous step). But, now that we don't use CPU's to do the TF, the benefit is less pronounced. It makes it simpler process-wise to do all of the TF (GPU's), then hand it off to P-1 (CPU's or some GPUs).

Does that clear it up enough?

[nemonusquam]

Originally Posted by AlexCara

First of all I apologize for my ugly english.
I'm a new forum's user at this moment just out of curiosity.
I red your post about the Exponent Status Report. Very clean explanation.
But.... I am searching for the status of each exponent.
May you help me?

There's also https://www.mersenne.ca/exponent/XXXXXXXX

nemonusquam

[jwnutter]

Thanks!

In regards to the first question, I still don't fully understand. That said, you've answered the question I just need to ponder on your response a bit and maybe it will come to me.

Yes, this definitely clears things up for me on the P-1 vs TF questions.

I also came up with another question regarding the Exponent Status Distribution. Specifically the values listed under Assigned and Available TF. https://www.mersenne.org/primenet/

It may be easiest to ask this question via an example. I see that the 111M exponent range has a range count of 53,816. And, as I understand from your previous post, this is the number of prime numbers between 111M and 112M-1 (though I still need to do some work to understand why). I also see that there are currently 14,220 TF assignments associated with this exponent range with none available. I'll come back to this in a moment.

My GPU is currently working on ~6,000 TF assignments in the 111M range. For all of the assigned values it appears to be testing a range from 2^73 to 2^74 (I selected "what make sense" when requesting these assignments). From these links https://www.mersenne.org/various/mat...rial_factoring and https://www.mersenne.org/report_expo...2918073&full=1 I can see that TF'ing is completed in stages (though the factoring cost appears to have changed slightly since this table was published based on my testing interval of 73 to 74 on exponents in the 111M range) with each stage generally assigned out over the course of many years (Moore's Law at work I assume).

Back to my example question. How are the various bit levels captured in the Assigned and Available TF data fields? In other words, what are the units of Assigned/Available TF? Is 1 Assigned TF equal to 1 Range Count in terms of units, if that makes sense? Or, is 1 Assigned TF equal to 1 bit level of 1 Range Count? I'm sorry these questions might not make any sense at all, but I'm trying to understand what I'm looking at in the Exponent Status Distribution vs. what my CPUs/GPUs are actually telling me they are working on at the moment.

I feel like I need to sit down with someone much more knowledgeable than myself for many many hours - each with beer in hand - and discuss a wide variety of GIMPS related topics that are still a bit fuzzy to me. That said, I am still learning by reading and asking questions on this forum. This team does a great job of supporting those of us that are interested in supporting the cause but are very ignorant of what's actually going on behind the curtains. And for that I thank you.

[nemonusquam]

Originally Posted by jwnutter

Thanks!

It may be easiest to ask this question via an example. I see that the 111M exponent range has a range count of 53,816. And, as I understand from your previous post, this is the number of prime numbers between 111M and 112M-1 (though I still need to do some work to understand why).

Go to https://www.browserling.com/tools/prime-numbers and ask to generate 53.816 primes starting at 111000000 and you will have all primes between 111M and 112M-1.

Those are "small" primes, fast to generate. Remember, the primes are from 111000007 to 111999997 and not from 2^111000007-1 to 2^111999997-1 which, if prime, is a Mersenne prime.

nemonusquam