How many of the primes (as in how many per cent) are concatenations (let us write $\oplus$ as the symbol for concatenation) of some other strictly smaller primes (in basis 10)? ( We are free to choose any split of the digits ).
For example
$$53 = 5 \oplus 3\\ 743 = 7 \oplus 43\\ 523 = 5\oplus 23$$
But $1103$ is not since $0$ is not a prime ( and say we choose to not allow numbers starting with $0$ as in $03$ )