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Colin, At the risk of sounding very stupid I've never understood what was actually meant by statements of the type "the primes appear to be distributed in a ma

Colin, At the risk of sounding very stupid I've never understood what was actually meant by statements of the type "the primes appear to be distributed in a manner indistinguishable from randomly". I say this because I imagine that the definition of what makes a prime a prime determines whether any particular number is prime or not. So what don't I get when people make statements like this? :(

ColinWright 13y ago
There's a classic experiment where you get people firstly to generate a length 50 "random" string of heads and tails by making it up. Then they genuinely flip a coin 50 times and write down the result. You can almost always tell the difference. there are statistical tests that you can apply that almost invariably identify which is which. So there are statistical tests that let us ask whether a particular collection is "random" (whatever that means) When we have the right model (the Cramer model is one) we can produce sequences of numbers which are genuinely created at random, but which the statistical tests cannot decide which sequences are the random ones, and which one is the primes. You can read a little here: http://www.solipsys.co.uk/new/RandomEratosthenes.html?HN1 http://www.solipsys.co.uk/new/RandomEratosthenes.html?HN1