> 2. Is overclocking of my Celeron 333 a good idea? I probably can't do
> it just now (EPoX P2-112A motherboard isn't made for such purposes),
> but I could upgrade it in about 2-3 months' time.
No. This can often lead to errors, and newer CPU's are on the edge of
sanity when it comes to heat anyway. I've heard that a Celeron can burn
it self out completely in a few minutes without a heat sink.
> 3. How are the expected completion date and the chance that "my"
> exponent is a prime computed?
The chance that your number is prime is computed using a conjecture of
Wagstaff which states that:
* The number of Mersenne primes less than or equal to x is about
(e^gamma/log 2) * log log x. (Here gamma is Euler's constant).
* The expected number of Mersenne primes 2^p-1 with p between x and
2x is about e^gamma.
* The probability that 2^p-1 is prime is about (e^gamma log ap )/(p
log 2) where a=2 if p=3 (mod 4) and a=6 if p=1 (mod 4).
gamma is Euler's constant, ~.577, it is computed as
(sum from 1 to n of 1/v)-ln(n))
> 4. How come there are 8180017 iterations for M8180017? Shouldn't
> there be (p - 2) iterations for Mp (since we know L(1) and don't need
> to know L(p))? Or am I missing somethig? Or do I just cavil at it,
> and it is useful to know which Mp am I checking for a first glance at
> Prime95 output (most probably)?
L(n) is defined as (2+sqrt(3))^n+(2-sqrt(3))^n. S(n)=L(2^n), hence
L(1)=S(0)=4. Just because we know what L(1) is doesn't mean it should
be discounted, it is still included in the count. We are trying to find
if S(p-1) mod Mp=0, if S(0)=4 then there are p iterations.
-Lucas
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