I would like to generate random numbers whose distribution mimics that of the primes. So the number of generated random numbers less than $n$ should grow like $n / \log n$, most intervals $[n,n+n^\epsilon]$ should contain approximately $n^\epsilon / \log n$ generated numbers (Selberg's short intervals), etc. Does anyone know of a computationally feasible method for generating such "look-a-like primes"?
Addendum. I implemented Henry and Xoff's suggestions. Here are several instances of the first ten "pseudoprimes": $ 4, 5, 9, 10, 17, 23, 27, 28, 31, 44 $ $ 7, 8, 9, 10, 12, 15, 18, 19, 27, 34 $ $ 6, 11, 15, 16, 23, 26, 27, 29, 45, 49 $ And here is the cumulative distribution pseudoprimes up to $10^6$ (red), together with a plot of $n / \log n$ (purple), for one random run: