I took prime $131$, squared digits of it and wrote them in natural order as they appear, from left to right, and obtained $191$, then I obtained $1811$ by the same procedure, and then $16411$ and then $1361611$, and $131,191,1811,16411$ are primes and $1361611$ is not.

To illustrate how to arrive at the next number in sequence from previous one, take, for example, $16411$.

We have: $1^2=1$ and $6^2=36$ and $4^2=16$ and $1^2=1$ and $1^2=1$ so we obtain $1361611$ from $16411$.

Can we generate in this way as large a number of different (to avoid loops like one that starts with $11$) primes as we want? Or there is some law/laws that do not allow that?