Problem 18

For some positive integer $n$, the prime factorisation of the number $n! = 1 \times 2 \times \ldots \times n$ is of the form shown below. $2 \times 3 \times 5 \times 7 \times 11 \times 13^4 \times 17 \times \ldots \times 41 \times 43 \times 47$ The primes are written in increasing order. Ink has covered some of the primes and some of the exponents. What is the exponent of 17?