Newer milestone thread - Page 311

ZacHFX · 2021-06-24, 18:28

Quote:

Originally Posted by Raydex

I'll admit that I was a little less clear in my earlier post today than I should have been. I will spend this post explaining the change I observed.

As kriesel pointed out, countdowns to Mersenne primes have been on the page for a long time; the Wayback Machine shows that it has been done at least as far back as 2008.

https://web.archive.org/web/20081218...rt_milestones/

The most recent "double-check milestone" to a Mersenne prime to be completed was on April 8, 2018, when verifications surpassed M(43112609), the 47th Mersenne prime. For most of the 3 years, 2 months, 15 days since then, the countdowns to verifying all exponents up to those of known Mersenne primes have appeared together in the bottom subsection of the "Progress toward next GIMPS milestones" section. To clarify what I mean by that subsection, here is what the page looked like three days ago, according to the Wayback link a couple of posts ago.

Countdown to verifying all tests below M(57 885 161): 3 154
Countdown to verifying all tests below M(74 207 281): 294 425
Countdown to verifying all tests below M(77 232 917): 349 899
Countdown to verifying all tests below M(82 589 933): 448 608

Now, this section contains only the last three bulleted countdowns, and the countdown for M(57885161) now appears in the section above it, right below the countdown to 57 million and right above the countdown to 58 million.

The fourth bullet, of course, wasn't added until December 21, 2018, after M(82589933) was discovered and officially published (because Mersenne primes are kept secret for a week or two after their discoveries, before being publicly identified in a press release). From December 21, 2018 until about five hours ago, the structure of the last section remained the same, with only the countdown totals after the colons changing over time.

I understood what you meant! I thought it wouldn't make the change until we cleared everything below 56m, so I was pleasantly surprised to read your post. I should be clearing 12-15 exponents per week until we confirm M48.

Uncwilly · 2021-06-24, 18:58

No need to fully quote the immediately preceding post to add a post of a couple of lines.

ZacHFX · 2021-06-24, 20:19

OK.

Uncwilly · 2021-06-28, 15:39

56,000,000 achievement unlocked.

Madpoo · 2021-07-06, 23:02

Quote:

Originally Posted by Uncwilly

I fixin on poaching the DC on that. I will run it as a PRP with cert.

Just FYI, if there are PRP+certs run on "smaller" exponents (I forget the size, but below 65-70M or so, wherever we were when PRP's first starting coming in for first time work) the numbers for milestones may be off.

I think I'd coded the double-check countdowns so they're still only looking at LL data, not the combined LL+PRP like the first time checks are.

At some point I'll have to fix it but I figured I still had years to do that. LOL I just naively assumed people would run LL DC's.

Well, and PRP+Cert wasn't even a think back then when we first started with the PRP assignments, so it would have made even less sense for someone to do a pair of PRPs when we already had one LL waiting for a matching residue.

Madpoo · 2021-07-06, 23:07

Quote:

Originally Posted by Raydex

...The countdown to M(57885161) now appears between the countdowns for 57000000 and 58000000....

You're welcome. That was me.

When I updated it for the last milestone and was adding in the next DC one, I figured it was a good time to move that M48 countdown to a more logical spot.

When the other primes get close to their double-checking ranges, I'll plan to do the same. Although I do have some time before worrying about it for the next one.

greenskull · 2021-07-12, 10:05

Hello everyone!

I haven't appeared here for a long time :)
Although from time to time I look through the research statistics with interest.

I have done some calculations and want to share it if appropriate here.
My calculations show that we will cross the level "All tests below 57885161 verified" around mid-November 2021, most probably on 22 of November.
And if another Mersenne Prime is not found before this level, then M (57,885,161) will get its proven №48.

x -- Julian dates, x = 44522 = November 22, 2021
y -- Mersenne exponents / 1000000
red -- all tests verified
blue -- tested at least once
purple -- prime discovered

https://www.mersenneforum.org/attach...1&d=1626083646

Large red ellipse -- 95%, ±120 days
Small red ellipse -- 50%, ±40 days

https://www.mersenneforum.org/attach...1&d=1626083742

But the main intrigue of the prediction is, of course, WHEN the next Prime Mersenne number will be found.
It seems to me that it is possible to build a game with bets on this :)

What's especially interesting is that the gap between the blue and red curves is growing exponentially. I believe that this leads to an increase in the probability of detecting the next Mersenne Prime in the phase of All tests. Although until now this has not happened yet.

It is interesting that the magenta trend tends to converge with the blue one. And it will probably cross it when the Mersenne Prime is found in the phase of All tests.
It is also interesting that the magenta trend is steadily increasing to the red by about x2 constant coefficient.
These factors can provide a basis for an approximate forecast of the timing of finding the next Mersenne Prime and even roughly estimate it.
All this is at the level of a hypothesis, of course :)

kriesel · 2021-07-12, 13:26

That's ~1.5 months later than the estimate in https://mersenneforum.org/showthread.php?t=26591&page=2 and consistent with completing the 58M milestone this year. You haven't shown the math basis of your estimate.

greenskull · 2021-07-12, 14:34

My previous forecast, which I gave here on April 04, 2019, regarding the crossing of this level was September 12, 2021 ± 45 days:
https://mersenneforum.org/showpost.p...5&postcount=12

Today on July 12, 2021 I have slightly corrected it to November 22, 2021.
Confidence intervals:
95%, ±120 days
50%, ±40 days

Basis is a regression model:
1) Exponential component with three parameters -- a, b, c
2) Two oscillating components -- d, e, f, g, h, i
Estimation of actual deviations from the model and calculation of the probability density function.

If anyone is interested:
y = a*(x+c)^b + d*sin((2*pi*x/e)+f)+g*sin((2*pi*x/h)+i)

a = 6.301777924391815E-08,
b = 2.214115161025356E+00,
c = -3.341476105126364E+04,
d = 8.211973595219082E-01,
e = 5.349108589075790E+03,
f = 1.818362727915368E+01,
g = 3.411798486806563E-01,
h = 2.832702528053284E+03,
i = -4.648139615289046E+00

Uncwilly · 2021-07-12, 14:42

Quote:

Originally Posted by knowhow

What's especially interesting is that the gap between the blue and red curves is growing exponentially. I believe that this leads to an increase in the probability of detecting the next Mersenne Prime in the phase of All tests.

Since you have not been around so much, there are a few factors to take note of.
The 'recent' sudden rise in throughput is due to massive amount of work being done by a single newer user. This has exaggerated the trend greatly.
The development of GEC has vastly reduced the error rate. So the likelihood of missing a Prime during FTC is now vanishingly small.
Using PRP with certs has now basically eliminated the need for double checks. So once the DCs get up near 100m they will rapidly speed their rate. They should catch up quite quickly.

Quote:

It is interesting that the magenta trend tends to converge with the blue one. And it will probably cross it when the Mersenne Prime is found in the phase of All tests.

It can only cross it if there was an erroneous test on the next prime. There are co few primes that the likelihood of one of them being a test with an error is very low. Tests that are reporting "bad" errors are routinely getting a DC far ahead of the tail end of the DC's. That further diminishes the chance of an overlooked prime waiting to be found by DC. It is reasonable for us to assume that the next MP is not going to be found via DC. Thus the magenta line will only intersect the other if the last exponent getting a FTC is the next FTC. Otherwise it will be above it. It is much more likely to be found were the bulk of the FTC results are being turned in.

greenskull · 2021-07-12, 15:48

Yes, thanks for the details.
Perhaps the purple curve will not cross the blue one, but will run parallel to the blue one and slightly above it with a little noise.

Regarding the confidence intervals I would even say
95%, ±82 days
50%, ±25 days.
The previous estimation of confidence intervals I gave for exponential approximation with no oscillations components.

I am using the shifting parameter (c) to build the model and let the curve fit in the best possible way, and this can neutralize the prediction error.
Again, the fact that a new outstanding player was involved into the game was probably repeated regularly in the past in one way or another, adjusted for time, and can be considered a certain natural factor that has already taken into account by such a complex oscillation model.

In any case, time will tell. Let's see how events will develop.

2021-07-12, 10:05	#3417
greenskull "greenskull" Apr 2019 2·3·5 Posts	When? Hello everyone! I haven't appeared here for a long time :) Although from time to time I look through the research statistics with interest. I have done some calculations and want to share it if appropriate here. My calculations show that we will cross the level "All tests below 57885161 verified" around mid-November 2021, most probably on 22 of November. And if another Mersenne Prime is not found before this level, then M (57,885,161) will get its proven №48. x -- Julian dates, x = 44522 = November 22, 2021 y -- Mersenne exponents / 1000000 red -- all tests verified blue -- tested at least once purple -- prime discovered https://www.mersenneforum.org/attach...1&d=1626083646 Large red ellipse -- 95%, ±120 days Small red ellipse -- 50%, ±40 days https://www.mersenneforum.org/attach...1&d=1626083742 But the main intrigue of the prediction is, of course, WHEN the next Prime Mersenne number will be found. It seems to me that it is possible to build a game with bets on this :) What's especially interesting is that the gap between the blue and red curves is growing exponentially. I believe that this leads to an increase in the probability of detecting the next Mersenne Prime in the phase of All tests. Although until now this has not happened yet. It is interesting that the magenta trend tends to converge with the blue one. And it will probably cross it when the Mersenne Prime is found in the phase of All tests. It is also interesting that the magenta trend is steadily increasing to the red by about x2 constant coefficient. These factors can provide a basis for an approximate forecast of the timing of finding the next Mersenne Prime and even roughly estimate it. All this is at the level of a hypothesis, of course :) Attached Thumbnails Last fiddled with by greenskull on 2021-07-12 at 10:15

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2021-06-24, 18:58	#3412
Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 2³×1,223 Posts	No need to fully quote the immediately preceding post to add a post of a couple of lines.

2021-06-24, 20:19	#3413
ZacHFX Mar 2017 Halifax, NS 17 Posts	OK.

2021-06-28, 15:39	#3414
Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 2³·1,223 Posts	56,000,000 achievement unlocked.

2021-07-12, 13:26	#3418
kriesel "TF79LL86GIMPS96gpu17" Mar 2017 US midwest 2·7·383 Posts	That's ~1.5 months later than the estimate in https://mersenneforum.org/showthread.php?t=26591&page=2 and consistent with completing the 58M milestone this year. You haven't shown the math basis of your estimate.

2021-07-12, 14:34	#3419
greenskull "greenskull" Apr 2019 30₁₀ Posts	My previous forecast, which I gave here on April 04, 2019, regarding the crossing of this level was September 12, 2021 ± 45 days: https://mersenneforum.org/showpost.p...5&postcount=12 Today on July 12, 2021 I have slightly corrected it to November 22, 2021. Confidence intervals: 95%, ±120 days 50%, ±40 days Basis is a regression model: 1) Exponential component with three parameters -- a, b, c 2) Two oscillating components -- d, e, f, g, h, i Estimation of actual deviations from the model and calculation of the probability density function. If anyone is interested: y = a(x+c)^b + dsin((2pix/e)+f)+gsin((2pi*x/h)+i) a = 6.301777924391815E-08, b = 2.214115161025356E+00, c = -3.341476105126364E+04, d = 8.211973595219082E-01, e = 5.349108589075790E+03, f = 1.818362727915368E+01, g = 3.411798486806563E-01, h = 2.832702528053284E+03, i = -4.648139615289046E+00

2021-07-12, 15:48	#3421
greenskull "greenskull" Apr 2019 2·3·5 Posts	Yes, thanks for the details. Perhaps the purple curve will not cross the blue one, but will run parallel to the blue one and slightly above it with a little noise. Regarding the confidence intervals I would even say 95%, ±82 days 50%, ±25 days. The previous estimation of confidence intervals I gave for exponential approximation with no oscillations components. I am using the shifting parameter (c) to build the model and let the curve fit in the best possible way, and this can neutralize the prediction error. Again, the fact that a new outstanding player was involved into the game was probably repeated regularly in the past in one way or another, adjusted for time, and can be considered a certain natural factor that has already taken into account by such a complex oscillation model. In any case, time will tell. Let's see how events will develop.