The Quest for the Largest Prime Number

Prime numbers are the loners of arithmetic: whole numbers greater than one that cannot be evenly divided

by anything except one and themselves. They start small—two, three, five,

seven, eleven—but refuse to settle into a tidy pattern. More than two thousand

years ago, Euclid proved there are infinitely many primes, so there can never

be a final one. The hunt, then, is for the largest known prime: the

biggest one humans have verified so far. Proof is the hard part; finding a

factor is easy, showing none exist is not. Most record winners are Mersenne primes,

built as two to the power p minus one, because they can be tested efficiently.