## Editorial for A Square Problem

Remember to use this editorial only when stuck, and not to copy-paste code from it. Please be respectful to the problem author and editorialist.

Submitting an official solution before solving the problem yourself is a bannable offence.

Author: Ninjaclasher

Note that $$a^2-b^2$$ is a difference of squares. This means it can be rewritten as $$(a-b)(a+b)$$.

From this, it can be proven that $$a^2-b^2$$ is only prime when $$a-b=1$$ and $$a+b$$ is a prime.

Thus, we can check if $$a+b$$ is prime to determine if $$a^2-b^2$$ is prime. To check if $$a+b$$ is prime, we can check if it is divisible by any numbers less than its square root. The proof is left as an exercise for the reader.

Time Complexity: $$\mathcal{O}(\sqrt{a+b})$$