Truncatable Primes

Recall that a prime is a positive integer with exactly two distinct divisors: $1$ and itself. We say that a number $a$ is a prefix of a number $b$ if $a$ can be obtained by deleting some number of digits from the end of $b$. For example, $1231$ is a prefix of $12314433$. A truncatable prime is a number all of whose prefixes of non-zero length are prime. For example, $23$ is a truncatable prime, because its non-empty prefixes $2$ and $23$ are both prime.

Given two positive integers $a$, $b$ ($a \le b$), write a program that determines how many integers in the closed interval $[a, b]$ are truncatable primes.

A single line of standard input contains two integers $a$, $b$ ($1 \le a \le b \le 10^{18}$), separated by a space.

Print a single integer: the number of truncatable primes that are not less than $a$ and not greater than $b$.

There are only finitely many such numbers. The first digit must be one of the single-digit primes $2$, $3$, $5$, $7$, and every time you append a digit on the right the resulting number must still be prime. So you can generate all such numbers in advance and then count those that fall inside the interval.