Prime Number Checker

A number is prime when nothing but 1 and itself divides it. Trial division only needs to test up to the square root — any factor above it pairs with one below. 97 survives tests by 2, 3, 5, and 7, and √97 < 10, so it's prime.

Euclid proved primes never run out, yet they thin gradually (about 1 in ln n near n). Their unpredictable spacing is unsolved mathematics — and their multiplication-easy, factoring-hard asymmetry secures modern encryption.