Suppose, an interval $[a,b]$ with positive integers $a<b$ is given.
Can we estimate the number of composite strong-probable primes to base $2$ in [a,b] ?
In particular, I am interested in estimating $N_k$, the number of $k$-digit composite strong-probable primes to base $2$. The $N's$ corresponding to $k=1,2,3,4,5,6,7$ are $0,0,0,5,11,30,116$, which I found out by brute force.
But $N_{40}$, for example, cannot be determined by brute force. And the Monte-Carlo-method will probably not give reasonable accurate values because the quotient $\frac{N_k}{9\cdot 10^{k-1}}$ , which is the probability that a random $k$-digit number is composite and strong-probable prime to base $2$, will probably decrease drastically with growing $k$.
Any ideas ?