There have historically been large gaps between Mersenne primes (all comparisons refer to their logarithms):
[LIST][*]M#13 is four times as large as M#12[*]M#15 is twice as large as M#14[*]M#21 is twice as large as M#20[*]M#28 is twice as large as M#27, which in turn is twice as large as M#26[*]M#32 is 3.5 times as large as M#31[*]M#36 is twice as large as M#35[*]M#39 is twice as large as M#38[/LIST]
It's entirely possible that M#48 is going to be in the, say, 100M range, or even higher. My sixth sense tells me that discovering it is truly going to test our patience.

[QUOTE=ixfd64;304493]There have historically been large gaps between Mersenne primes (all comparisons refer to their logarithms):[/QUOTE]:no:
That is nice, but based upon the GIMPS era primes, it is not unlikely that 48, 49, and 50 lie below 60,000,000. Currently it looks like most of the new LL work is being done between 45 - 55,000,000.

[QUOTE=LaurV;304468]That remembered me when I was young and stupid and I put a clothes pin on the tail of the cat.. She was turning and turning and turning, like a tornado, and getting angrier and angrier and noisier and noisier... Someone you know?[/QUOTE]Yep.
Now leave off her tail and put a bowl of milk in front of her.

[QUOTE=Uncwilly;304504]but based upon the GIMPS era primes...[/QUOTE]

Irrelevant. Our run of good luck has no impact on the probabilities for the next gap size.

[QUOTE=Prime95;304508]Irrelevant. Our run of good luck has no impact on the probabilities for the next gap size.[/QUOTE]... if certain conjectures are correct.

[QUOTE=Prime95;304508]Irrelevant. Our run of good luck has no impact on the probabilities for the next gap size.[/QUOTE]

[QUOTE=cheesehead;304520]... if certain conjectures are correct.[/QUOTE]
Best summed up in one word: Poisson.

Expected new primes <60M is currently ~0.3

Probability of no more primes <60M is e[SUP]-0.3[/SUP] = 0.74

David

PS Bear this in mind when reading Crandall's obligatory page
[url=http://primes.utm.edu/notes/faq/NextMersenne.html]"Where is the next Mersenne Prime?"[/url]

[QUOTE=davieddy;304531]Bear this in mind when reading Crandall's obligatory page
[url=http://primes.utm.edu/notes/faq/NextMersenne.html]"Where is the next Mersenne Prime?"[/url][/QUOTE]

I think you meant Caldwell not Crandall.

[QUOTE=Prime95;304534]I think you meant Caldwell not Crandall.[/QUOTE]
Close but no cigar:smile:

D

[QUOTE=LaurV;304468]That remembered me when I was young and stupid and I put a clothes pin on the tail of the cat.. She was turning and turning and turning, like a tornado, and getting angrier and angrier and noisier and noisier... Someone you know?[/QUOTE]

[QUOTE=davieddy;304506]Yep.
Now leave off her tail and put a bowl of milk in front of her.[/QUOTE]
To pursue this analogy further:
a bowl of full creamed milk may tempt her more than a trough of skimmed.

What is the range of n for each interval?

[QUOTE=henryzz;304548]What is the range of n for each interval?[/QUOTE]Having taught physics, I can guess what you are on about.
log ("exponent") is ~ 1.48

Hope that helps.

D

PS It takes years to appreciate the distinction between a log and an exponent.