Re: [PrimeNumbers] The randomness of prime numbers?
- --- On Wed, 4/17/13, bobgillson@... <bobgillson@...> wrote:
> All the odd numbers not listed are the primes - so how canThey can't. The people who use the word "random" in the context of prime numbers either:
> they arise randomly from a non random logical process?
a) know what they're talking about, and are trying to make a subtle point that you're overlooking; or
b) don't know what they're talking about.
The simplest statement that's closest to the truth that ascribes the "random" feature to the primes is probably:
Given a large enough range of significantly larger numbers (say 10^100 .. 10^100+10^10, for example), the density of primes in that range is as one would expect from a random variable (whose distribution I could state, and which is parametrised by the size of the numbers).
Primes are to randomness what Pointilism is to brushstrokes.
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- On 4/17/2013 10:36 AM, bobgillson@... wrote:
> I have often seen in print that prime numbers are random.Jack:
> Ignore such assertions; even if they are in print, they are wrong. Think about it -- every time you enumerate the prime numbers, you get the same result. That's the opposite of random. :)Indeed, there is nothing random about the primes. You can make a nice mechanical device to find them based on the sieve...
What they are trying to say is bit more complicated, usually one of the following: that parts of their behavior can be modeled using randomness (E.g., Erdos-Kac theorem); and/or, that they often "do" things that surprise us. (E.g., how can something with this much variation come out of a notion as mechanical as the primes?)