Establish the following test for primes.
If $n$ is odd, greater than $5$, and there exist relatively prime integers $a$ and $b$ such that $a — b = n$ and $a + b = p_1\cdot p_2\cdot... p_k$ (where $p_1, p_2 , . . . , p_k$ are the odd primes less than $\sqrt n$ ), then $n$ is prime.