for the last 4 hrs, 240 minutes, 268 blocks were found.
How does this sound Jorge?
I understand that block finding is a Poisson process where the probability of finding a block in any small interval of time
dt seconds long is
dt/
T where
T is the mean time between blocks. Then, the probability of
n blocks being found in an interval with length
t is
exp(-
t/
T)*(
t/
T)^
n/
n!
In your example,
t/
T is 240 and we want the probability of
n being 268 blocks or more. The answer is
exp(-240)*sum(k=268..oo 240^k/k!
That is not easy to compute, but for those range of values the distribution should be close to a Gaussian distribution with mean 240 and standard deviation sqrt(240). So we can instead compute the probability of a standard Gaussian variable (mean 0, variance 1) being greater than
r = (268 - 240)/sqrt(240). I can't compute that right now, will do that later...
Forgive me if I'm wrong but would that analysis not require the assumption of constant hashrate/difficulty over the period considered? If there is a sharp rise or fall in hashrate over the period then you will end up with some very improbable results.