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Old 2021-10-06, 09:23   #1
firejuggler
 
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Default Let's finish primality verification through Mp#49*, M(74 207 281)

To this day, 2021-10-06, we have proved that Mp#48 is indeed in the right place.


So, considering the speed of progresssion of the last 6 month (about 20k), it will take us about
7 to 8 years to get to MP#49



Countdown to verifying all tests below M(74 207 281): 268 808


I'm targetting first half of 2029.


[edit]Related previous thread: https://www.mersenneforum.org/showthread.php?t=26591

Last fiddled with by Uncwilly on 2021-10-06 at 13:31
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Old 2021-10-06, 09:28   #2
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Congratulations!!!
It's time to add another term for http://oeis.org/A000043!
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Old 2021-10-06, 10:57   #3
greenskull
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Perfectly!
I just love this forum :)

Soon I will give my forecast for the timings.
This will be M60000000, M65000000, M70000000 and of course M74207281 with a confidence interval of 85%.
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Old 2021-10-06, 11:50   #4
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My Magic Crystal Ball tells me that all exponents below 74 207 281 will be tested and verified by
March 08, 2025 Β± 64 days (85%).

Click image for larger version

Name:	MagicCrystalBall_color.jpg
Views:	29
Size:	131.0 KB
ID:	25869

Accordingly:
M60000000 - May 12, 2022
M65000000 - May 28, 2023
M70000000 - May 23, 2024

Place your bets gentlemen.

Last fiddled with by greenskull on 2021-10-06 at 11:52
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Old 2021-10-06, 12:41   #5
Dr Sardonicus
 
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Quote:
Originally Posted by firejuggler View Post
First post on march with 20k test left.
so that's about 6 month.
number of test left to MP#49 is around 270 k
Thats 13.5 * 6month... lets add a bit of time because tests take longer.. and we're looking at 7 or 8 years.
I'd say it's a perfectly reasonable initial estimate. Nothing fancy, just extrapolating on the current rate of progress, with an adjustment for larger exponents taking longer to test. I suppose the current rate of progress and the amount of extra time the larger exponents will require could be quantified a bit more precisely, but the emphasis here is on "a bit."

As mentioned earlier in this post in the "countdown to M57885161" thread, I had over two years previously used simple extrapolation for an ETA to M57885161 without even adjusting the rate of progress for larger exponents. It proved to be accurate beyond my wildest expectations.

It is of course possible that things will happen in the future to change the rate of progress - e.g. faster computing hardware or methods, or hordes of new users joining the project - but such things are imponderable at present. If things do happen that significantly change the rate of progress, the estimate can and IMO should be revised accordingly.
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Old 2021-10-06, 13:04   #6
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Quote:
Originally Posted by Dr Sardonicus View Post
I had over two years previously used simple extrapolation for an ETA to M57885161 without even adjusting the rate of progress for larger exponents. It proved to be accurate beyond my wildest expectations.
Maybe you will try to hit the bull's-eye again? :)
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Old 2021-10-06, 13:42   #7
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Quote:
Originally Posted by greenskull View Post
Maybe you will try to hit the bull's-eye again? :)
firejuggler beat me to it. The method I would use is essentially the same as he used. As I said, it might be possible to tweak it a bit, but IMO it isn't worth the effort.

It would be silly at this point to try to make a precise prediction for an ETA. As I have already indicated, a lot could happen to change the rate of progress in the coming days and years. We don't know whether it will, or if it does, what it might be or how much it might affect the rate of progress.

I don't take these estimates seriously enough to wager on them. I do take soundness of method seriously. In this case, it seems to me that simple extrapolation of the current rate of progress is a good place to start. It is based on what I call the "assumption of ignorance." Apart from larger exponents requiring more computation to test, we are at present ignorant of any factors that will change the rate of progress appreciably. If we in future learn some reason why present trends will not continue, we revise the estimate accordingly.

One presently known factor that might affect the rate of progress slightly is the replacement of first time LL testing with PRP testing with cheap verification. There are AFAIK still unconfirmed LL tests in the pipeline. As those are cleared, things could speed up a bit.

Other imponderables besides the ones I already mentioned are possible changes in how the project works: Assignment rules could be changed. Methods might be found to prevent people from deliberately impeding progress. And so on.
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Old 2021-10-06, 13:50   #8
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Quote:
Originally Posted by firejuggler View Post
To this day, 2021-10-06, we have proved that Mp#48 is indeed in the right place.
Someone should tell Prof. Chris Caldwell about this so he can update his site/database.
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Old 2021-10-06, 14:03   #9
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The sign of mastery is the ability to repeat it. Otherwise, it's just a coincidence.
This is just an interesting game, there is nothing wrong with a mistake. We learn from mistakes.

For example, my short distance M#48 forecast was purely technical and did not take into account fundamental factors. This is because I have just started to learn the essence of the work of the GIMPS project.

The understanding the fundamental factors and step triggers can give a tangible advantage at close distances, but comes down to statistical noise at long distances.

The long distance is advantageous to me or anyone who is capable of using a more complex extrapolation model than the parabolic one ;)

Come on!

Last fiddled with by greenskull on 2021-10-06 at 14:05
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Old 2021-10-06, 14:32   #10
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Quote:
Originally Posted by greenskull View Post
The understanding the fundamental factors and step triggers can give a tangible advantage at close distances, but comes down to statistical noise at long distances.
If you believe that there is still a significant gap in your understanding.

Last fiddled with by kriesel on 2021-10-06 at 14:33
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Old 2021-10-06, 15:44   #11
Dr Sardonicus
 
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Quote:
Originally Posted by greenskull View Post
The sign of mastery is the ability to repeat it. Otherwise, it's just a coincidence.
This is just an interesting game, there is nothing wrong with a mistake. We learn from mistakes.

For example, my short distance M#48 forecast was purely technical and did not take into account fundamental factors. This is because I have just started to learn the essence of the work of the GIMPS project.
I don't know what "fundamental factors" is supposed to mean.

The question here is when a specific computational task will be completed. It seems to me that the "fundamental factor" in answering that question is the rate of progress.

IMO it's analogous to estimating how long it will take to get to a faraway place (here on Earth of course!). How your conveyance works may be "fundamental," but knowing that doesn't help much in giving an ETA. Knowing the total distance to your destination, and the average speed you can maintain, do allow such an estimate, irrespective of any details of how you are moving - be it swimming, walking, running, bicycling, driving, or by aircraft.

I accurately estimated when the exponents up to 57885161 would be cleared, two and a half years in advance, without knowing anything about how the work was being assigned, how the computations are done, or any other "fundamental factors." All I knew was how fast exponents were currently being cleared. I did a simple linear extrapolation.

At the moment, I don't know a better basis for a predicition. If you think you do, it is incumbent upon you to explain why you think it is better.
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