On Sunday 01 October 2006 07:22, [EMAIL PROTECTED] wrote: > 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."
That's obviously wrong - though (over reasonable intervals) the density of prime numbers is approximately uniformly distributed when plotted against the _logarithm_ of the interval midpoint. > > 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). Ah, but knowledge of the first few prime numbers _does_ influence prediction of later ones in the sequence ... if P is a prime number, we know that kP is composite for all integers k > 1 (by definition!) > Since the Eratosthem sieve algorithm can produce the list of all prime > numbers, prime numbers do not appear randomly. Yes. > Since knowing all primes below sqrt(P) can be used to prove that P is prime > or not, prime numbers do not appear randomly. Yes. > Large prime numbers seems to appear randomly to us because they would > require computers and time as big as our Universe. Sorry but I don't understand this. In fact the universe is finite in content and time whereas the set of positive integers (and primes) is infinite so I don't see how any computer could possibly be big or fast enough to tabulate all primes. Not even a quantum computer. > > So: prime numbers are not distributed randomly. By definition: _NO_ particular list of numbers can _POSSIBLY_ be random! Regards Brian Beesley _______________________________________________ Prime mailing list [email protected] http://hogranch.com/mailman/listinfo/prime
