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