Let $k$ be a positive integer and $N$ a random $k$-digit number. Suppose $N$ is strong probable prime to base $2$.
What is the probability $p_k$ that $N$ is composite ?
There are infinite many composite strong-probable-primes to base $2$, but the density of such numbers decreases heavily. Is there a good approximation (ot at least an asymptotic formula) for $p_k$ ?
The smallest composite $2$-sprp is $2047$, so $p_k=0$ for $k\le 3$
There are $1066$ $2$-sprps with $4$ digits. $5$ of them are composite, hence $p_4=0.004690$
There are $8374$ $2$-sprps with $5$ digits. $11$ of them are composite , hence $p_5=0.001314$
There are $68936$ $2$-sprps with $6$ digits. $30$ of them are composite, hence $p_6=0.000435$
There are $586197$ $2$-sprps with $7$ digits. $116$ of them are composite, hence $p_7=0.000198$