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-   -   [Mission Accomplished] Let's finish primality verification through Mp#48*, M(57 885 161) (https://www.mersenneforum.org/showthread.php?t=26591)

masser 2021-09-23 14:31

[QUOTE=Uncwilly;588432]

Or other things can happen....[/QUOTE]

:goodposting::popcorn:

kriesel 2021-09-23 14:42

[URL="https://quoteinvestigator.com/2013/10/20/no-predict/"]Prediction is hard, especially about the future.[/URL]

greenskull 2021-09-23 22:37

[QUOTE=kriesel;588472]which states in part:
...
later in date predicted.:reality-check::deadhorse:[/QUOTE]
I will read it when I take a vacation and have more spare time :)

PS The forecast error is best taken into account depending on the distance from which the forecast was made.
Since making a error for a couple of weeks from a distance of 1 year and from a distance of 1 month are completely different things.

tuckerkao 2021-09-24 00:58

[QUOTE=greenskull;585849]My prediction is November 22, 2021
95%, ±82 days
50%, ±25 days

Let's see :)[/QUOTE]
There are only 17 outstanding exponents left until M[SUB]#48[/SUB] becomes official, so the prediction has been really accurate.

Wouldn't it be easier if other users just run the PRP tests for these exponents, less likely to encounter the Gerbicz errors than the Jacobi errors.

Uncwilly 2021-09-24 01:23

[QUOTE=tuckerkao;588522]Wouldn't it be easier if other users just run the PRP tests for these exponents, less likely to encounter the Gerbicz errors than the Jacobi errors.[/QUOTE]:picard:

kriesel 2021-09-24 02:03

[URL="https://www.mersenneforum.org/showpost.php?p=533167&postcount=5"]required reading[/URL]

tuckerkao 2021-09-24 02:09

[QUOTE=kriesel;588525][URL="https://www.mersenneforum.org/showpost.php?p=533167&postcount=5"]required reading[/URL][/QUOTE]
Encounter Jacobi errors in LL are much more likely than Gerbicz errors in PRP. Also the PRP certifications of those exponents won't take longer than 1 hour for most users.

LaurV 2021-09-24 02:35

Methink encountering errors has nothing to do with what math you use to spot the error and to recover from that error. Errors pop up if you have shitty hardware, or try to push it too hard.

Happy5214 2021-09-24 12:25

[QUOTE=tuckerkao;588526]Encounter Jacobi errors in LL are much more likely than Gerbicz errors in PRP. Also the PRP certifications of those exponents won't take longer than 1 hour for most users.[/QUOTE]

I would have guessed the opposite. On bad hardware, Gerbicz should catch [I]more[/I] errors than Jacobi (key word is [I]catch[/I]; the actual number of bad iterations should be roughly equal either way), but also have the ability to correct the bad iterations more efficiently (wrt granularity/frequency of checks and the probability of an error being caught), thus producing more reliable results.

firejuggler 2021-09-24 14:09

Lets hope it id before the new year, and i'll be happy.

kriesel 2021-09-24 14:29

[QUOTE=Happy5214;588566]Gerbicz should catch [I]more[/I] errors than Jacobi (key word is [I]catch[/I]; the actual number of bad iterations should be roughly equal either way), but also have the ability to correct the bad iterations more efficiently (wrt granularity/frequency of checks and the probability of an error being caught), thus producing more reliable results.[/QUOTE]Correct. [URL="https://en.wikipedia.org/wiki/Jacobi_symbol"]Jacobi symbol [/URL]check is done infrequently, only ~twice a day because it is computationally costly. Its detection rate is only ~50% of errors. If done after every LL iteration it would cost more than it might save, and still only detect ~75% of errors. For Mersennes it yields +1 or -1 IIRC; there are only 3 possible values in general, 1, -1, 0, so an error going undetected is quite probable. [URL="https://mersenneforum.org/showpost.php?p=465033&postcount=30"]This post[/URL] describing the Jacobi symbol check led to some quick implementation, and consideration of what other checks might be available.
[URL="https://www.mersenneforum.org/showpost.php?p=465431&postcount=88"]Robert Gerbicz' post[/URL] describing the check for PRP followed days later. Both Jacobi and GEC are typically applied by the software authors to use around 0.2% of computing time by default, with some user control for more or less cost & frequency.

Gerbicz' check is highly effective, since it can return one of a great many values, and only one will match.
Empirically, PRP/GEC has shown ~24ppm error in completed tests, ~800 times lower than LL. And some of that error count was from outside / after the GEC check, handling the final residue produced. Prime95 got hardened against that after some such errors were identified. See [url]https://www.mersenneforum.org/showpost.php?p=509940&postcount=4[/url]
These number-theory based checks are in addition to and independent of other inexpensive measures, such as round-off magnitude checking, or sum of inputs vs. sum of outputs.


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