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). Since the Eratosthem sieve algorithm can produce the list of all prime numbers, prime numbers do not appear randomly. Since knowing all primes below sqrt(P) can be used to prove that P is prime or not, prime numbers do not appear randomly. Large prime numbers seems to appear randomly to us because they would require computers and time as big as our Universe. So: prime numbers are not distributed randomly. See: http://en.wikipedia.org/wiki/Random_number http://en.wikipedia.org/wiki/Chaitin%E2%80%93Kolmogorov_randomness http://www.cs.auckland.ac.nz/CDMTCS/chaitin/sciamer.html Regards, Tony _______________________________________________ Prime mailing list [email protected] http://hogranch.com/mailman/listinfo/prime
