Eccoci.

The divisors of $12$ are: $1,2,3,4,6$ and $12$.
The largest divisor of $12$ that does not exceed the square root of $12$ is $3$.
We shall call the largest divisor of an integer $n$ that does not exceed the square root of $n$ the pseudo square root ($\operatorname{PSR}$) of $n$.
It can be seen that $\operatorname{PSR}(3102)=47$.

Let $p$ be the product of the primes below $190$.
Find $\operatorname{PSR}(p) \bmod 10^{16}$.