# Cramer's random model for the primes

Cramer's random model of the primes asserts, roughly speaking, that the primes behave as if every large integer n had an independent probability of $1/\log n$ of being prime (as predicted by the prime number theorem).
Cramer's random model predicts the Hardy-Littlewood prime tuples conjecture. Another prediction is that the number of primes in an interval $[n,n+\log n]$ for large generic n should asymptotically obey a Poisson distribution. This motivates Cramer's conjecture.