The next Mersenne prime
 

Ok, here it goes, make your bets. I vote 1.

It's smaller than 13M and I will be the one discovering it through doublechecking. :D

there are greater odds in the higher exponents, because we havn't started to check that area:ernst: .

[QUOTE][i]Originally posted by E_tron [/i]
[B]there are greater odds in the higher exponents, because we havn't started to check that area:ernst: . [/B][/QUOTE]

I agree. I'm betting option three, as are most other people (over 60% of votes).

Why did I choose the :ernst: ? I meant to use the :innocent: .

Check the Status page. Notice that the range where M40 was found has a 0.53 probability of finding a prime. The range from 40250000 to 50000000 has a 0.56 probability which means M41 most likely would be in that range.

Finding M40 in the range 20.4M-25.35M has no effect on the probability of adjacent Mersenne numbers being prime. There are [I]still[/I] 0.53 primes expected in that range. Also you can add up all the expected primes below 40.25M and you get 1.87 expected new primes. So the next prime is most likely below 40.25M.

What exactly do you mean by "the next Mersenne prime"?
Is it

(a) the next that GIMPS (or anybody else) finds
or
(b) the lowest existing Mersenne prime that is yet to be uncovered?

I.e. the next prime we find might be well above the magical 10 million digit line (case a) even though there might be a lower one left (case b).

:bounce: Bump :bounce:
:banana: Bump :banana:

[QUOTE][i]Originally posted by Spaceman_Spiff [/i]
[B]What exactly do you mean by "the next Mersenne prime"?
Is it

(a) the next that GIMPS (or anybody else) finds
or
(b) the lowest existing Mersenne prime that is yet to be uncovered?[/B][/QUOTE]
In the absence of flava's specific qualification, I think (a) is the intended interpretation. Consider the situation at the time just prior to discovery of the primality of M20996011. Suppose one were again considering the question: What is the next Mersenne prime? Now skip back to the present. Didn't "M20996011" turn out to be the correct answer to that earlier question because it was the chronologically next one discovered? If one prefers (b), then that earlier question has not yet been answered.

[QUOTE][B]I.e. the next prime we find might be well above the magical 10 million digit line (case a) even though there might be a lower one left (case b).[/B][/QUOTE]
Hmmm... Desn't your use of "next" in that example imply that you yourself think (a) is the correct interpretation?:smile:

:banana: Bump :banana:
bump :bounce: bump