Merry Christmas and a prime! (M50 related)

[Mark Rose]

Originally Posted by chalsall

Turns out the acceptance email was actually from an experimental AI "story picker" they are working on.

The submission is now on SlashDot! "News for Nerds, stuff that matters."

Quipped one Anonymous Coward:

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

[rudy235]

Originally Posted by Dubslow

Well if you ignore the less-than-optimal choice of metaphor, the underlying statement of opinion is extremely valid. This is surely an extremely unlikely find, at least in the context of the standard hypotheses about the Mersenne distribution.

I remember reading somewhere that Clarkson (the discoverer of the 37th prime) was not very enthused when he was assigned the exponent 3021377 because it was too close to the previously discovered Mersenne Prime with exponent 2976221

It came to be the closest pair of consecutive Mersenne exponents. 1.52% apart. In this recent case the difference between the exponents is less tight 4.08%. Previously there have been consecutive Mersenne Prime exponents separated by a smaller percentage. Between the 20th and the 21st Mersenne's exponents 9941 and 9689 the difference was 2.60% The difference between the 46th? and 47th? Primes is 3.55%

On January 27th, 1998, all this work came together--after many days of computer time, Clarkson found this record Mersenne prime on his home computer! When the PrimeNet server chose this exponent for him to test, Clarkson did not want to test it. "I never would have imagined two Mersenne primes would be so close together!" he said. He went ahead anyway and found the smallest gap yet (in terms of percentage) between any two Mersenne primes. The actual test took about 46 days while running part-time on a 200-MHz Pentium computer. (It would have taken about a week if the computer was working full-time.)

[Dubslow]

Originally Posted by rudy235

I remember reading somewhere that Clarkson (the discoverer of the 37th prime) was not very enthused when he was assigned the exponent 3021377 because it was too close to the previously discovered Mersenne Prime with exponent 2976221

It came to be the closest pair of consecutive Mersenne exponents. 1.52% apart. In this recent case the difference between the exponents is less tight 4.08%. Previously there have been consecutive Mersenne Prime exponents separated by a smaller percentage. Between the 20th and the 21st Mersenne's exponents 9941 and 9689 the difference was 2.60% The difference between the 46th? and 47th? Primes is 3.55%

I'm talking larger scale issues, notably the aforementioned fact that the 8-digit range has nearly doubled the Mersenne count of all previous ranges. That's a real stumper. My reaction would be the same if it's a 77M exponent or a 90-95M exponent. A ~150M-200M exponent being the next prime would be far less surprising.

[Madpoo]

Originally Posted by rudy235

...The difference between the 46th? and 47th? Primes is 3.55%

Well... who knows? Maybe even less? We still haven't verified the placement of M46 and M47... they're only tentative. LOL Could find another one somewhere in-between!

In fact, when I'm not picking up triple-checks to resolve, I thought I'd try and hurry up the countdown to verifying M46's placement.

[Prime95]

Originally Posted by Dubslow

I'm talking larger scale issues, notably the aforementioned fact that the 8-digit range has nearly doubled the Mersenne count of all previous ranges. That's a real stumper. My reaction would be the same if it's a 77M exponent or a 90-95M exponent. A ~150M-200M exponent being the next prime would be far less surprising.

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.

[dragonbud20]

Originally Posted by chalsall

And, also, extremely unlikely. People tend to run GIMPS for very specific reasons.

The "glory". Ensuring the sanity of the hardware they are responsible for. Space heaters....

that last one may or may not be why I only send TF results in the winter...

[CRGreathouse]

Originally Posted by Madpoo

FYI, this goes back to my hint here:
My hints

I didn't want to be too specific because some clever person might analyze all the potential candidates to see which one had 10 nines in a row somewhere, to narrow it down.

Of course, I think Mark's hints were a little too on the nose, giving the first digit as well as the last two. That and knowing the FFT sizes we were talking about, plus a couple other tidbits were basically a dead giveaway.

I hadn't seen that the last two digits were known, that narrows the field by a factor of 10 (since only 08, 12, 28, 32, 48, 52, 68, 72, 88, and 92 can occur). Knowing the first digit is 4 narrows it by a factor of log(10)/log(1.25) ~ 10. So from 551318 candidates (we can't trust the database here, there's usually skulduggery) we'd expect about 5000-6000. Actually 6734 remain after those tests, it seems that the first digit gives more like a factor of 7 in practice.

[Madpoo]

Originally Posted by CRGreathouse

I hadn't seen that the last two digits were known, that narrows the field by a factor of 10 (since only 08, 12, 28, 32, 48, 52, 68, 72, 88, and 92 can occur). Knowing the first digit is 4 narrows it by a factor of log(10)/log(1.25) ~ 10. So from 551318 candidates (we can't trust the database here, there's usually skulduggery) we'd expect about 5000-6000. Actually 6734 remain after those tests, it seems that the first digit gives more like a factor of 7 in practice.

The first digit being 7 and last two digits being 17 were in reference to the exponent, not the decimal expansion (in case my mention wasn't clear).

Based on that, and how many unchecked exponents currently live between 76e6 and 80e6 that end in 17, there are only 412 candidates... exponents that don't have an LL test or factor.

There may have been other clues that would narrow it down more, but a pool of only 412 exponents (as of right now anyway) is getting a lot closer.

Oh, I forgot, we have PRP results now in that range, and 10 of those candidates have PRP tests, so it's really only a pool of 402 exponents.

[rudy235]

Yes, that is even a better example of closeness.

43112609 1.0109935791

[pacionet]

One of Italian main newspaper press release:

http://www.corriere.it/scienze/18_ge...5ccceb4d.shtml

[ET_]

Originally Posted by pacionet

One of Italian main newspaper press release:

http://www.corriere.it/scienze/18_ge...5ccceb4d.shtml

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.