Hi all,
I had to be out of town for a week. I'll catch up on my email
and the stats pages as soon as possible. Thanks for your patience.
At 04:12 PM 3/7/99 -0000, [EMAIL PROTECTED] wrote:
>1. Does anyone know where the estimate of an exponent yielding a Mersenne
prime
>that Prime95 outputs in its status pop-up comes from?
Remember, I'm a layman mathematician so don't be too hard on me!
This comes from the observation that the chance of finding a factor
between 2^x and 2^(x+1) is 1/x.
Now assume we are looking at M1000 and we know from trial factoring
that it has no factors below 2^50. The chance that M1000 is prime
is the chance that it has no 51 bit factor (50/51) times the chance that
it has no 52 bit factor (51/52) times .... the chance that it has no
500 bit factor (499/500). You'll note a lot of these terms cancel leaving
the formula:
chance of prime = how far factored / (exponent/2)
= 2 * how far factored / exponent
BTW if you couple this with the formula for frequency of primes
you get the expectation of 1.78 Mersenne primes between exponents Y and 2*Y
Another BTW, real mathematicians have told me the 2 in the above formula
should really be Euler's constant.
>2. Does our continued effort in eliminating possible Mersenne primes
change that
>estimate in any way?
No. Each test is an independent event.
> Since I joined the project 10 months ago, we have found no
>new Mersenne primes
We have been unlucky.
Best regards,
George
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