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2008-06-20, 10:31   #8
davieddy

"Lucan"
Dec 2006
England

6,451 Posts

Quote:
 Originally Posted by axn1 And what is the probability that no primes would be found between now and 4456213.62? EDIT:- What happens if you take Geometric Mean (or use log of the ratios?)
This is analogous to Mersenne primes: a plot of log(n) against
the rank order of each prime fits a straight line well.
We conjecture from this that the expected number of primes between
n1 and n2 is c*ln(n2/n1).
If we take n2/n1 to be your average ratio, we choose c such that
the expected number of primes is one.
We can use this to construct a poll where the ranges represent
the 25% percentiles. The four ranges offered in the poll are:
n<a
a<=n<b
b<=n<c
c<=n
The "fair" choice of ranges has a
75% chance of no primes before a
50% chance of no primes before b
25% chance of no primes before c

The construction of this fair poll (or one with more options)
gives the clearest possible answer to "where is the next prime" IMO.

David

Last fiddled with by davieddy on 2008-06-20 at 11:06