How many of the primes can be subdivided into concatenations of smaller primes?

56 Views Asked by At

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 $03$ )