We shall define a sqube to be a number of the form, p²q³, where p and q are distinct primes.
For example, 200 = 5²2³ or 120072949 = 23²61³.

The first five squbes are 72, 108, 200, 392, and 500.

Interestingly, 200 is also the first number for which you cannot change any single digit to make a prime; we shall call such numbers, prime-proof. The next prime-proof sqube which contains the contiguous sub-string "200" is 1992008.

Find the 200th prime-proof sqube containing the contiguous sub-string "200".