Given two integers n and m. Check n^2 – m^2 is prime or not. n and m can be very large.
Input : n = 6, m = 5 Output : YES Input : n = 16, m = 13 Output : NO
A simple solution is to fist compute n^2 – m^2, then check if it is prime or not. n^2 – m^2 might be very large – it might not even fit into 64-bit integer. Checking primality for it certainly cannot be performed naively.
A better solution is to express n^2 – m^2 as (n-m)(n+m). This is prime if and only if n-m = 1 and n+m is a prime.
Time Complexity: O(sqrt(n+m))
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