Prime-Worthy Primes

Let a subcat of a number be defined for positive integers such that for any number of $n$ digits,

• There are $n - 1$ subcats.

• The first subcat is the units digit.

• The second subcat is the number formed by the tens and units digits combined, and so on.

• Any number isn't its own subcat.

Thus, say, for a number $5347$ , there are $3$ subcats, namely: $7$ , $47$ , and $347$ .

Now, we call an $n$ -digit number to be Prime-Worthy if all subcats $X_k$ of $X$ of length $k<n$ are nonzero and prime, regardless of whether or not $X$ itself is prime or not. It is mandatory though for subcats to exist for it to be considered Prime-Worthy.

How many Prime-Worthy primes are there less than $10000$ ?