Merry Christmas and a prime! (M50 related)

[pacionet]

Originally Posted by ET_

I sent the press release to "Le Scienze" (the Italian section of Scientific American), Focus and Rudi Mathematici.They hopefully will publish something in their next monthly issue.

I sent the press release to Google Doodle, maybe they will consider to use it (maybe on December 26, 2018 or January 3, 2019)

[ramgeis]

Originally Posted by pacionet

I sent the press release to Google Doodle, maybe they will consider to use it (maybe on December 26, 2018 or January 3, 2019)

September 1st and September 8th 2018 would be also nice candidates. https://en.wikipedia.org/wiki/Marin_Mersenne

[Spherical Cow]

The news is certainly getting around- this is a screen shot of the first thing I saw when I hit the Chrome button on my phone this morning to check on the news of the world...the next articles below it were North and South Korea possibly meeting, Bannon and Trump, etc. etc.

Norm

[chalsall]

Originally Posted by Mark Rose

If GIMPS Can Find Such a Huge Prime
Just think how big a prime PHOTOSHOPS could find!

Yeah, I found that quite funny!

Originally Posted by Spherical Cow

The news is certainly getting around...

Indeed! The Register posted quite a good article this morning, for example.

I'm always interested in seeing the variety in quality in coverage. Even though the press release was edited quite carefully, some "News" coverage is completely off the mark.

[Mini-Geek]

Originally Posted by Mark Rose

...Things like summing the digits or hashing the number or its decimal expansion are brute-forceable, so I didn't want to post those...

If you hash not just the exponent itself, but the exponent plus a message and/or nonce, then you have a secure hash.

E.g. if I post the SHA256 hash

8b51abad469fced362fe5119034c0c598665458f4bc441a85eeb05f008fce0f5

you'd never be able to tell that the message was:

The exponent is 77,232,917 and my name is Tim and here's some random junk: jfidosajfoipdsajhfuhbgdfsiuh4re78wayfg4e3vrjn8u743o

But

ad7b5d1347152d5fd403062aa18e1fa7abdda84ed45ce412b4dd9966cd58b0ee

could be brute-forced rather easily back to "77232917".

[Mini-Geek]

Originally Posted by Prime95

Indeed. Look at this table showing percentage difference from the previous Mersenne prime exponent.

24036583	1.1448166511
25964951	1.0802263783
30402457	1.1709036924
32582657	1.0717113094
37156667	1.1403817374
42643801	1.1476756244
43112609	1.0109935791
57885161	1.3426503833
74207281	1.2819741661
77232917	1.0407727646

That is 10 consecutive Mersenne primes where the percentage gap is less than the expected long-term average of 1.47576 (see http://primes.utm.edu/notes/faq/NextMersenne.html )

P.S. Note we also beat Clarkson's 2.9M to 3.0M minimum percentage gap.

A related post, http://www.mersenneforum.org/showpos...&postcount=513 shows that beating the gap 10 consecutive is .63^10 or 1 in a 100 event.

I have a strong feeling that some mathematician smarter than I will one day have a solid conjecture or theorem for the distribution of Mersennes being rather higher than our current conventional knowledge. I am well-acquainted with random chance in prime-finding, but I think there's got to be a point where we say "maybe we were wrong" and investigate it further.


Also since I've yet to say it: congratulations to Jon Pace and to all GIMPS participants!! These are always exciting finds, but to have finally reached 50 is a nice milestone.

[chalsall]

Another excellent and extremely well researched article at the Smithsonian.

[MisterBitcoin]

The german media is not giving so much attention then is suggested.
German "science news" spektrum is normaly very detailed, well this is a little bit short:
http://www.spektrum.de/news/23-3-mil...tellen/1530507

IT news site "heise": https://www.heise.de/newsticker/meld...n-3933986.html

The IT site "golem", which I wrote an larger mail yesterday, did´t post anything about it, yet.
Normal german news paper, like Focus, Zeit or "Bild" ("news paper", funny I know) wrote an online article about it. We should also see it in the printed versions.

[xilman]

Originally Posted by Madpoo

In the future, the hints should be a little more subtle.

Frankly, my dear, I don't give a damn.

For years now I've made absolutely no attempt whatsoever either to predict an unknown exponent nor to analyze in any way what ever hints may have been given.

There are slightly less tedious ways to pass my time.

[chalsall]

Originally Posted by xilman

Frankly, my dear, I don't give a damn.

Completely agree. But the point stands...

For those who /do/ know the exponent should be much more careful about the hints they give. Or, perhaps, just say nothing at all.

[CRGreathouse]

Originally Posted by Mini-Geek

I have a strong feeling that some mathematician smarter than I will one day have a solid conjecture or theorem for the distribution of Mersennes being rather higher than our current conventional knowledge. I am well-acquainted with random chance in prime-finding, but I think there's got to be a point where we say "maybe we were wrong" and investigate it further.

I wonder about this too. I think it was two Mersenne primes ago that I pointed out that the spacing seemed tighter than explained by the standard heuristic, and it's tighter still today (even if there are no Mersenne primes hiding between the known ones).

The basic idea of the heuristic is to treat Mersenne numbers as random integers of their size with no prime factors below 2k + 1 or 6k + 1, but really they're much more restricted than that in terms of divisors. It's not crazy to think that the effect would be to change the leading term or throw in a large second term (like in the Lemke Oliver & Sound paper).