The Riemann Hypothesis, often declared to be the number one outstanding unsolved question in mathematics, usually takes some explaining to describe accurately to a layperson. I like the equivalence, recently proved by Jeffrey Lagarias of AT&T Research, of the Riemann Hypothesis to the following Statement: Statement: ------------------------------------------------------------------------------ ------------------------------------------ For any n = 1,2,3,... let sigma(n) = the sum-of-divisors function (so that for example sigma(6) = 12), and let H_n = 1 + 1/2 + 1/3 + ... + 1/n be the nth harmonic number. Let log denote log_e. Then for all n = 1,2,3,..., (*) sigma(n) <= H_n + exp(H_n) * log(H_n) ------------------------------------------------------------------------------ ------------------------------------------. Lagarias adds the words "with equality only for n = 1". I suspect it's easy to prove that for n > 1 the RHS of (*) is never an integer, but maybe a number theorist out there can confirm this. --Dan A.