The Riemann hypothesis is a statement about a mathematical curiosity known as the Riemann zeta function. That function is closely entwined with prime numbers — whole numbers that are evenly divisible only by 1 and themselves. Prime numbers are mysterious: They are scattered in an inscrutable pattern across the number line, making it difficult to predict where each prime number will fall (SN Online: 4/2/08).
But if the Riemann zeta function meets a certain condition, Riemann realized, it would reveal secrets of the prime numbers, such as how many primes exist below a given number. That required condition is the Riemann hypothesis. It conjectures that certain zeros of the function — the points where the function’s value equals zero — all lie along a particular line when plotted (SN: 9/27/08, p. 14). If the hypothesis is confirmed, it could help expose a method to the primes’ madness.Emily Conover, “Here’s why we care about attempts to prove the Riemann hypothesis” at Science News
See also: Prime numbers are not “nearly as scattershot” as previously thought