Fun with a false positive

Madpoo · 2016-06-26, 02:39

The system to email people when a prime is reported is working.

Too bad it was a false positive this time around... George thinks it's because it was an old version that would so something like that if the save file had some issue or another (I probably just mangled his story). Prime95 25.11 I think it was.

M43232521

Anyway, the email system worked.

Prime95 · 2016-06-26, 04:35

Quote:

Originally Posted by Madpoo

Anyway, the email system worked.

Well, the backup system worked. The primary system probably failed as I think it is supposed to send to a wide audience when a likely prime is submitted and to a limited audience when a prime with a highly suspect error code is submitted.

Uncwilly · 2016-06-26, 06:01

Are all of those Anon's that started checks the same as the one that reported the bad LL?

NBtarheel_33 · 2016-06-26, 07:13

What an incredible cluster of primes that would have been: M42643801, M43112609, and M43232521. Shame it was a false positive!

GP2 · 2016-06-26, 08:39

If you start tinkering with the alert system, one useful thing to add would be a check and alert for Mersenne factors that are Wieferich primes (or maybe this check is already done?).

When a factor f is found, it can be verified by testing that 2^p (mod f) = 1. Presumably the server does this each time a factor is reported, to filter any bogus results.

It is trivial to also check 2^p (mod f²). If this is ever also equal to 1, then f would be only the third known Wieferich prime and we would also have the first known non-square-free Mersenne number with prime exponent p.

Since each factor found nowadays is at least 61 bits, they are all well beyond the exhaustive-search limit for Wieferich primes which I believe has reached somewhere on the order of 10¹⁷. So each new Mersenne factor found is like a lottery ticket (with about the same improbable odds) for a chance to make a momentous discovery. In fact, sometimes I wonder if this is the motivation behind user TJAOI's quest to find second-and-higher factors of already-factored exponents.

The odds are very low, maybe astronomically low, but modular exponentiation is so rapid that the entire database of tens of millions of factors can be checked in minutes (and I've already done so). So this would be a useful thing to add, both at mersenne.org and at mersenne.ca for exponents higher than 1 billion, assuming that it's straightforward to add a call to the alert system code.

S485122 · 2016-06-26, 11:09

Quote:

Originally Posted by Madpoo

...
M43232521
...

Are there plans to restore the hidden (because of primeness) history for that exponent ?

Jacob

retina · 2016-06-26, 11:37

Quote:

Originally Posted by S485122

Are there plans to restore the hidden (because of primeness) history for that exponent ?

All the LL history seems to be here:

http://www.mersenne.org/report_ll/?e...dispdate=1&B1=

The error code was 0019174C

S485122 · 2016-06-26, 13:31

Quote:

Originally Posted by retina

All the LL history seems to be here:

http://www.mersenne.org/report_ll/?e...dispdate=1&B1=

The error code was 0019174C

Indeed, it is there but not on the page the OP linked to. It must have to do with the code to hide a newly found Mersenne Prime.

Jacob

GP2 · 2016-06-26, 14:30

Quote:

Originally Posted by S485122

Indeed, it is there but not on the page the OP linked to. It must have to do with the code to hide a newly found Mersenne Prime.

Jacob

No, that page is good too, at least it is now. Try refreshing your cache.

S485122 · 2016-06-26, 20:43

Quote:

Originally Posted by GP2

No, that page is good too, at least it is now. Try refreshing your cache.

It is not important but the History section of that page still does not display the false result. In the that section there should be an entry for 2016-06-23 and there is not.

Madpoo · 2016-06-27, 21:32

Quote:

Originally Posted by S485122

Are there plans to restore the hidden (because of primeness) history for that exponent ?

Well, I guess... try this: http://www.mersenne.org/report_expon...3232521&full=1

The trick there was only showing a history if "is prime!" if that result ended up being bad or has been verified and publicly announced.

As retina pointed out, the LL specific report shows more info such as the actual error code which is probably more interesting than a false "Mxxx is prime!" entry.

2016-06-26, 02:39	#1
Madpoo Serpentine Vermin Jar Jul 2014 5×677 Posts	Fun with a false positive The system to email people when a prime is reported is working. Too bad it was a false positive this time around... George thinks it's because it was an old version that would so something like that if the save file had some issue or another (I probably just mangled his story). Prime95 25.11 I think it was. M43232521 Anyway, the email system worked.

2016-06-26, 08:39	#5
GP2 Sep 2003 5035₈ Posts	Wieferich primes If you start tinkering with the alert system, one useful thing to add would be a check and alert for Mersenne factors that are Wieferich primes (or maybe this check is already done?). When a factor f is found, it can be verified by testing that 2^p (mod f) = 1. Presumably the server does this each time a factor is reported, to filter any bogus results. It is trivial to also check 2^p (mod f²). If this is ever also equal to 1, then f would be only the third known Wieferich prime and we would also have the first known non-square-free Mersenne number with prime exponent p. Since each factor found nowadays is at least 61 bits, they are all well beyond the exhaustive-search limit for Wieferich primes which I believe has reached somewhere on the order of 10¹⁷. So each new Mersenne factor found is like a lottery ticket (with about the same improbable odds) for a chance to make a momentous discovery. In fact, sometimes I wonder if this is the motivation behind user TJAOI's quest to find second-and-higher factors of already-factored exponents. The odds are very low, maybe astronomically low, but modular exponentiation is so rapid that the entire database of tens of millions of factors can be checked in minutes (and I've already done so). So this would be a useful thing to add, both at mersenne.org and at mersenne.ca for exponents higher than 1 billion, assuming that it's straightforward to add a call to the alert system code.

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2016-06-26, 06:01	#3
Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 10892₁₀ Posts	Are all of those Anon's that started checks the same as the one that reported the bad LL?

2016-06-26, 07:13	#4
NBtarheel_33 "Nathan" Jul 2008 Maryland, USA 5·223 Posts	What an incredible cluster of primes that would have been: M42643801, M43112609, and M43232521. Shame it was a false positive!