Prime Number Checker

How it works

A prime number has exactly two divisors: one and itself. Two, three, five, seven, eleven — and two is the only even prime, since every other even number is divisible by two. One is deliberately excluded. It has only a single divisor, and admitting it would break the fundamental theorem of arithmetic, which says every integer above one factors into primes in exactly one way. With one allowed, 6 could be 2×3 or 1×2×3 or 1×1×2×3, and uniqueness would collapse. Primes are the atoms of the integers, and they thin out without ever running out — Euclid proved there are infinitely many. Their difficulty is now infrastructure: modern encryption rests on the fact that multiplying two large primes is easy while recovering them from the product is, so far as anyone knows, not.