Prime Number Checker & Factoriser

Because a prime has exactly two distinct divisors, one and itself, and 1 has only one. The definition is chosen deliberately: if 1 were prime, every number would have infinitely many prime factorisations and the fundamental theorem of arithmetic would fail.

Only to the square root. If a number has a factor above its square root, it must have a matching factor below it, which the search would already have found. That reduces testing a million from a million steps to a thousand.

RSA encryption rests on the fact that multiplying two large primes is easy while factoring the product back is not. The security of a great deal of internet traffic is exactly that asymmetry.