M40 Again!!!! - Page 10

sdbardwick · 2003-12-01, 18:40

WOO HOO!!

Now I can't wait to see who won the M40 "pool"....

Prime Monster · 2003-12-01, 18:41

Quote:

Originally posted by Prime95
The verification of M40 completed yesterday - success! Congratulation everyone.

I've been without Internet access for 2 days, so please forgive the late post. This was a bad time to move!

Scott has been coordinating the press announcement. I expect he'll tell me to announce the exponent on mersenne.org in the next 48 hours.

Hint: GIMPS data miners are very clever.....

Congratulation George, the unknow cruncher

, the project and everyone

Prime Monster

PrimeCruncher · 2003-12-01, 19:39

Ooh, ooh! Is it 20996011? Was I right?

flava · 2003-12-01, 19:43

Yes! I knew this one is goning to be prime. Can't wait to see the exponent.

Merlin · 2003-12-01, 19:54

Quote:

Originally posted by PrimeCruncher
Ooh, ooh! Is it 20996011? Was I right?

I hope so, because one of my boxen is 99.80% done with an exponent slightly bigger than that, and I have irrationally optimistic hopes for it to be M41.

edorajh · 2003-12-01, 19:56

YES!!!

Congratulations to actual discoverer of new Mersenne prime, George, Scott and all GIMPSters who patiently contribute their time and energy to this exciting research.

GP2 · 2003-12-01, 20:52

Quote:

Originally posted by Merlin
I hope so, because one of my boxen is 99.80% done with an exponent slightly bigger than that, and I have irrationally optimistic hopes for it to be M41.

On "average", the exponent of each Mersenne prime is expected to be 1.4756 times larger than the previous one (more precisely, the "geometric mean of the ratio of two successive Mersenne exponents is 2^{1/e[sup]gamma}[/sup], where gamma is Euler's constant 0.57721566490153286...).

The plausible range for the current M40 actually fits this ratio reasonably well with respect to M39. But the previous ratios of M39/M38 and M38/M37 were 1.93 and 2.31

So in an irrational "gambler's fallacy" sort of way, maybe we're due for the next Mersenne exponent to be discovered relatively close... maybe it will be less than 25M, who knows?

The plot of http://opteron.mersenneforum.org/png/log2_log2_Mn.png also suggests we ought to be heading back towards the green "expectation line" (ie, more primes rather than less in our future).

Worst-case scenario would be another gap like 216091 to 756839... in the current context, that would correspond to no primes until 75M! But the two previous times there was a big jump like that (127 -> 521 and 216091 -> 756839), the previous point was right on the green line, and right now we're well above that line already.

philmoore · 2003-12-01, 22:46

Two big ifs:

IF the new exponent is larger than 19,873,956, and IF this new Mersenne is eventually verified to be the 40th Mersenne prime in order of size, (a process which may take a few years), THEN this will be the first time that we have ever seen three gaps in a row with the ratios of the Mersenne exponents p(n+1)/p(n) all greater than the theoretically suggested mean 2^(e^-gamma), about 1.47576. Coincidental? Could be. Or maybe there is a reason that Mersennes thin out faster than the linear theory predicts. At any rate, it is obvious that we have been looking the past six years in territory that is a little thinner in Mersenne primes than we would have expected, which just makes the latest discovery all the sweeter!

ET_ · 2003-12-01, 23:48

Congratulations George.

Congratulations, Scott.

Congratulations, everybody!

Luigi

E_tron · 2003-12-02, 01:51

...this is the part where we wait. Will our guesses be correct? Will we ever know? Will we ever unglue ourselves from our computers?

Tune in tomorrow for the answers.

Fusion_power · 2003-12-02, 02:37

As to predicting the next Mersenne prime, if we follow the gaps from the previous numbers then we will have another in the 27million range.

Here's hoping! and congratulations

2003-12-01, 22:46	#107
philmoore "Phil" Sep 2002 Tracktown, U.S.A. 3·373 Posts	Two big ifs: IF the new exponent is larger than 19,873,956, and IF this new Mersenne is eventually verified to be the 40th Mersenne prime in order of size, (a process which may take a few years), THEN this will be the first time that we have ever seen three gaps in a row with the ratios of the Mersenne exponents p(n+1)/p(n) all greater than the theoretically suggested mean 2^(e^-gamma), about 1.47576. Coincidental? Could be. Or maybe there is a reason that Mersennes thin out faster than the linear theory predicts. At any rate, it is obvious that we have been looking the past six years in territory that is a little thinner in Mersenne primes than we would have expected, which just makes the latest discovery all the sweeter! Last fiddled with by philmoore on 2003-12-01 at 22:47

2003-12-01, 18:40	#100
sdbardwick Aug 2002 North San Diego County 5×137 Posts	WOO HOO!! Now I can't wait to see who won the M40 "pool"....

2003-12-01, 19:39	#102
PrimeCruncher Sep 2003 Borg HQ, Delta Quadrant 2·3³·13 Posts	Ooh, ooh! Is it 20996011? Was I right?

2003-12-01, 19:43	#103
flava Feb 2003 1110110₂ Posts	Yes! I knew this one is goning to be prime. Can't wait to see the exponent.

2003-12-01, 19:56	#105
edorajh Oct 2003 Croatia 1C8₁₆ Posts	YES!!! Congratulations to actual discoverer of new Mersenne prime, George, Scott and all GIMPSters who patiently contribute their time and energy to this exciting research.

2003-12-01, 23:48	#108
ET_ Banned "Luigi" Aug 2002 Team Italia 2·3·11·73 Posts	Congratulations George. Congratulations, Scott. Congratulations, everybody! Luigi

2003-12-02, 01:51	#109
E_tron Sep 2002 Austin, TX 3·11·17 Posts	...this is the part where we wait. Will our guesses be correct? Will we ever know? Will we ever unglue ourselves from our computers? Tune in tomorrow for the answers.

2003-12-02, 02:37	#110
Fusion_power Aug 2003 Snicker, AL 7×137 Posts	As to predicting the next Mersenne prime, if we follow the gaps from the previous numbers then we will have another in the 27million range. Here's hoping! and congratulations