Can anyone please verify/review this counterexample?

[SammyS]

Did you try $34$?

Whether you you try n=34 or some other candidate as a counter example, try to be systematic.

To see if some integer, $n$ is a counterexample, begin with $a=0$ and increment $a$ by $1$ while $a^2<n$. For each value of $a$, compute $p_a$ where $p_a=n=a^2$.
For a given number $n$, if all $p_a$ are composite (Neither prime, nor 1), then you have found a counter example.

Furthermore, consider using as candidates for $n$, non-prime numbers of the form $n=3k+1$. . You should find that using such a number for $n$ will generate a list of values for $p_a$ in which 5 of every 6 entries is divisible by 2 or 3 (or both).