What are the chances that M44 isn't M44?
 

If I'm not mistaken, the largest Mersenne known not to have any unknown Mersenne primes below it is M39, the rest have at least a chance of getting their status knocked up a notch. What I'm wondering is what are the chances that M44 isn't M44, \M43 isn't M43, and so on to M40.

Look at the expected new primes column at [url]http://www.mersenne.org/status.htm[/url]. This should get you close to the right answer.

According to my calculations based on the link Prime95 gave, M44 not being M44 is about 8.525%, M43 not being M43 is about 4.525%, M42 not being M42 is about 1.525%, M41 not being M41 is about 1.025%, and M40 not being M40 is about 0.525%.

If the expected number of new primes is 0.08, we obtain the
probability of finding no primes from the Poisson distribution:
e[sup]-0.08[/sup] = 0.923
So the probability of finding one or more primes is 7.7%

Is that the technique you used?

David

[quote=davieddy;101837]If the expected number of new primes is 0.08, we obtain the
probability of finding no primes from the Poisson distribution:
e[sup]-0.08[/sup] = 0.923
So the probability of finding one or more primes is 7.7%

Is that the technique you used?

David[/quote]
No, that's not what I used. I assumed that 0.08 expected primes meant they expect a 8% chance of finding a prime, and worked it that way. Although now that I think about it, that wouldn't make much sense, because at the bottom is says 2.56 and it is impossible to be over 100% sure that there would be a prime.

Don't try to get too accurate with your estimates. My numbers are based on some assumptions about error rates that could be off by 25 or even 50%.

[quote=Mini-Geek;101847]No, that's not what I used. I assumed that 0.08 expected primes meant they expect a 8% chance of finding a prime, and worked it that way. Although now that I think about it, that wouldn't make much sense, because at the bottom is says 2.56 and it is impossible to be over 100% sure that there would be a prime.[/quote]

Your way works approximately when the chance of two or
more primes is small (as in the case we are considering).
e[sup]-2.56[/sup] = 0.0773.
This is the probability that there won't be any more primes
below 79,000,000.

David

Having checked, the total expected primes with exponents
below 79,300,000 is in fact 2.14.
This give e[sup]-2.14[/sup] = 0.118 or 11.8% chance of no primes.

[quote=Prime95;101851]Don't try to get too accurate with your estimates. My numbers are based on some assumptions about error rates that could be off by 25 or even 50%.[/quote]

George (assuming it is thee), don't get me started on the optimal
error rate thread again:smile:

David

Looks to me like M44 will be the real M44

[QUOTE=deretsigernU;355151]Looks to me like M44 will be the real M44[/QUOTE]
Sure, but look at the vintage of the original thread!