[QUOTE=Batalov;422133]Gotta keep up with the Joneses![/QUOTE]

Use the force, George....

Having been one of those false positives, I am glad that wasn't prematurely trumpeted

[QUOTE=airsquirrels;422136]Having been one of those false positives, I am glad that wasn't prematurely trumpeted[/QUOTE]

Well, see, I wasn't going to name any names... :smile:

There are other funky false positives though. Right now there's only one that's still unverified (I ran one check, it needs a triple-check). So if anyone was interested...
[URL="http://www.mersenne.org/M62891251"]M62891251[/URL]

Here are the false positive counts broken down by year:
[CODE]Year Count
==== =====
2010 2
2011 4
2012 8
2013 1
2014 1
2015 2[/CODE]

[QUOTE=Batalov;422030]If we take the first 40 M-primes and do a linear regression of log[SUB]2[/SUB] log[SUB]2[/SUB] M[SUB]n[/SUB] ~ n, then the 95% confidence interval for the slope's estimate is (0.557, 0.587) and both Wagstaff's and Eberhart's conjectured slopes are within this CI.
Recall that Wagstaff's [TEX]\hat{\beta_1} = {1 \over {e ^ \gamma }} = 0.561458...[/TEX], while Eberhart's = log[SUB]2[/SUB] 3/2 = 0.5849625...

If we take the first 48 known M-primes, then the 95% confidence interval for the slope's estimate is (0.5366, 0.5659) and Wagstaff's is in 95% CI, but Eberhart's is not (in other words, Eberhart's, of "K-Y", conjecture can be rejected at 95% confidence level).

If we take the first 49 known M-primes, then the confidence interval slides slightly lower still, but Wagstaff's is still in the 95% CI, and Eberhart's can be rejected with slighly higher confidence level. (Note that if there exist "missed" M-primes, the slope will be lower still.)
[snip][/QUOTE]

Thanks, Serge - is it further reasonable to assume that the same kinds of "strong law of small numbers" effects which make it a foregone conclusion that the smallest 4 M(p) will all be prime based on the required form of the candidate factors (and nearly so for the smallest five Fermat numbers, of which just F_4 has a valid candidate factor, and just onesuch) will likely skew the statistics at the lower end? If so, it would make sense to throw out the smallest (say) ten M(p) and redo the fitting exercise with just the larger ones.

[QUOTE=Madpoo;422141]There are other funky false positives though. Right now there's only one that's still unverified (I ran one check, it needs a triple-check). So if anyone was interested...
[URL="http://www.mersenne.org/M62891251"]M62891251[/URL]
[/QUOTE]

I'll do it since I was poking at it earlier. It's in the queue for next week.

There is a very good reason to hide the exponent (beside the excitement this causes for some members here, and the fun of the hunt in itself), and that is to avoid two hundred users running double checks, and causing a "loss" for the project. Most of you guys have so much itch on your hands that you would temporarily abandon all the work you currently do, to test if the new mersenne prime is really prime, and then (if you are lucky to have a fast system) will scream all around that [U]you[/U] verified the new number and it is prime. :razz:

Luckily in the past I never was able to guess the exponent, hehe. :wink:

I remember for the last one I had to beg to some guy here to tell me the exponent (I posted on the forum about the fact that someone gave it to me, at that time) and when he did, I didn't run the test because first of all I didn't want someone to blame him for de-conspiring the exponent to me, and second, I wasn't sure he didn't just played along, giving me a false number :razz:, until the official result was announced. In spite of having one of the fastest systems at the time. And generally, when you already know the exponent, it does not seem so fun to run the test. But hunting is fun. Until now, I never double checked any exponent (of a prime mersenne) higher than 859433 (and that only as a test for cudaLucas.

Even if someone told me the number right now, I would not LL it. There's no point.

[QUOTE=Madpoo;422141]Well, see, I wasn't going to name any names... :smile:

There are other funky false positives though. Right now there's only one that's still unverified (I ran one check, it needs a triple-check). So if anyone was interested...
[URL="http://www.mersenne.org/M62891251"]M62891251[/URL]

Here are the false positive counts broken down by year:
[CODE]Year Count
==== =====
2010 2
2011 4
2012 8
2013 1
2014 1
2015 2[/CODE][/QUOTE]
Given that the type of result is marked as "C", not "P", I will hazard a guess that the last 2 digits of the residue are 02, not 00, and is most likely a hardware error - as described in the "Erroneous values of s_n" topic, if a hardware error causes the intermediate residue to become zero at any point, the next value in the sequence will be -2, and then that will become +2, and then +2 will keep reproducing itself from then on.

[QUOTE=Batalov;422073]It would serve as an excellent hook for the perennial theme "What's the use of all these Mersenne Prime searches?"[/QUOTE]

See [url=http://math.stackexchange.com/a/804304/1778]my answer on math stackexchange[/url]. :smile:

[QUOTE=ixfd64;422125]George said there wasn't a reason to hide the exponent after M42,643,801 was discovered: [url]http://www.mersenneforum.org/showpost.php?p=176012&postcount=50[/url]
[/QUOTE]

Reading closely, George said:
[QUOTE=Prime95;176012] I agree that[B] hiding the fact[/B] that a potential[B] prime has been found[/B] is not necessary.[/QUOTE]

So, not the new prime itself, just that a new one exists (probably).

[QUOTE=CRGreathouse;422176]See [url=http://math.stackexchange.com/a/804304/1778]my answer on math stackexchange[/url]. :smile:[/QUOTE]

Looking at the reply under yours would raise an interesting camel scenario with mersenne primes of this size.