Is there a way to pick a $k$ such that $p_0p_1 + ik$ is always a product of two primes? where $p_0, p_1$ are primes, $k < pq$, and $i = 0,1,2,3....$. In other words, you pick $k$ such that no matter what $i$ I use, $p_0p_1 + ik$ is still a product of two primes.
I tried with many examples, and saw that it always failed but I can't prove it logically. Would anyone give me a hint? Thanks in advance.