20160626, 02:39  #1 
Serpentine Vermin Jar
Jul 2014
3×11×101 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. 
20160626, 04:35  #2 
P90 years forever!
Aug 2002
Yeehaw, FL
29×277 Posts 
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.

20160626, 06:01  #3 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
3·3,581 Posts 
Are all of those Anon's that started checks the same as the one that reported the bad LL?

20160626, 07:13  #4 
"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!

20160626, 08:39  #5 
Sep 2003
A1B_{16} 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 f^{2}). 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 nonsquarefree Mersenne number with prime exponent p. Since each factor found nowadays is at least 61 bits, they are all well beyond the exhaustivesearch limit for Wieferich primes which I believe has reached somewhere on the order of 10^{17}. 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 secondandhigher factors of alreadyfactored 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. 
20160626, 11:37  #7  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2·3,301 Posts 
Quote:
http://www.mersenne.org/report_ll/?e...dispdate=1&B1= The error code was 0019174C 

20160626, 13:31  #8  
"Jacob"
Sep 2006
Brussels, Belgium
5·367 Posts 
Quote:
Jacob 

20160626, 14:30  #9  
Sep 2003
13·199 Posts 
Quote:


20160626, 20:43  #10  
"Jacob"
Sep 2006
Brussels, Belgium
5×367 Posts 
Quote:


20160627, 21:32  #11  
Serpentine Vermin Jar
Jul 2014
3×11×101 Posts 
Quote:
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. 

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