

A probabilistic model of prime numbers based on network theory - ColinWright
http://arxiv.org/abs/1402.3612

======
thearn4
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_...](http://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test)).
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.

~~~
Sniffnoy
That'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
Another 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.

