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Haven't had a chance to read the paper yet (though I do like both number theory and network theory, so it'll be on my to-do list). But if anyone is interested i
by thearn4 13y ago
Haven't had a chance to read the paper yet (though I do like both number theory and network theory, so it'll be on my to-do list). But if anyone is interested in a probabilistic notion of primality, the best practical example out there is the Miller-Rabin test (http://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test http://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_...). This describes the function that sits behind most `is_prime()` methods that you'll find in technical computing libraries.
Fun fact: it becomes a deterministic test if the generalized Riemann hypothesis is ever proven.
- ColinWright 13y agoThere's a different concept relating randomness and primes, and that's the model of the primes being distributed randomly. You can read more about that here: http://www.solipsys.co.uk/new/RandomEratosthenes.html?HN2 http://www.solipsys.co.uk/new/RandomEratosthenes.html?HN2
- Sniffnoy 13y agoThat's not really the same sort of "probabilistic notion of primality". This isn't about a test for primality; this is about a probabilistic model of the primes, where we replace the actual primes by a randomly-generated subset of the natural numbers that we believe ought to have similar properties. The basic one is the Cramér model, where we say that n is prime with probability 1/(log n), and these are independent of one another. This is giving a more complicated such model which it claims agrees better with the statistics of the actual primes.
- nilkn 13y agoAnother point of this model is, unlike Cramér's, it doesn't assume the prime number theorem as an entry point but rather displays it as a naturally derived property.