On Monday 02 October 2006 21:15, Mike McCarty wrote: > [EMAIL PROTECTED] wrote: > > Hi, > > > > Robert Betts said: "I meant to add that all the prime numbers are known > > to be distributed randomly--I repeat--randomly along the real line." > > > > Why "randomly" ? > > If I remember well, a set of numbers is random if the shortest way to > > describe it is to provide the list of these numbers (there is no > > algorithm to compute them, and knowing the first N numbers does not help > > to predict number numbered N+1). > > [snip] > > This is not any of the definitions of randomness I learned when I > was a grad student in Mathematical Probability and Statistics.
Isn't statistical testing about the probability that a number of samples are drawn from the same population? If I remember my statistics correctly, statistics doesn't actually define randomness itself, it merely describes a method for testing whether a finite sample of observations might have been drawn from a truly random infinite population, to a given confidence level. Do the digits in the decimal expansion of pi (3.14159...) constitute a random sequence? All known statistical tests appear to be passed at a high confidence level, if a sufficiently large sample is taken - yet the sequence is not random, any more than the digits in the decimal expansion of unity (1.00000...) are random, and for exactly the same reason - both 1 and pi are explicit unique values on the real number line. Regards Brian Beesley _______________________________________________ Prime mailing list [email protected] http://hogranch.com/mailman/listinfo/prime
