The Building Blocks

Every whole number greater than 1 is either prime (divisible only by 1 and itself) or composite (breakable into smaller primes). This clean split gives mathematics its structure. The number 2 is the only even prime — every other even number has 2 as a factor, so it can never have just two divisors.

Want to find every prime up to 100 by hand? Use the sieve of Eratosthenes, invented over 2,000 years ago. List the numbers 2 through 100. Circle 2, then cross out every multiple of 2. Circle the next uncrossed number, 3, and cross out its multiples. Repeat with 5 and 7. Whatever survives is prime. It is still the fastest way to sweep out small primes.