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Old 2008-06-20, 10:31   #8
davieddy's Avatar
Dec 2006

6,451 Posts

Originally Posted by axn1 View Post
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:
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.


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