--description--

We shall define a sqube to be a number of the form, ${p^2}{q^3}$, where $p$ and $q$ are distinct primes.

For example, $200 = {5^2}{2^3}$ or $120072949 = {{23}^2}{{61}^3}$.

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.

--hints--

primeProofSqubeWithSubString() should return 229161792008.

assert.strictEqual(primeProofSqubeWithSubString(), 229161792008);

--seed--

--seed-contents--

function primeProofSqubeWithSubString() {

  return true;
}

primeProofSqubeWithSubString();

--solutions--

// solution required