An improved bound for the de Bruijn-Newman constant Andrew Odlyzko AT&T Labs - Research amo@research.att.com The Riemann Hypothesis is equivalent to the conjecture that the de Bruijn-Newman constant LAMBDA satisfies LAMBDA <= 0. However, so far all the bounds that have been proved for LAMBDA go in the other direction, and provide support for the conjecture of Charles Newman that LAMBDA >= 0. This paper shows how to improve previous lower bounds and prove that -2.7 / 10^9 < LAMBDA. This can be done using a pair of zeros of the Riemann zeta function near zero number 10^{20} that are unusually close together. The new bound provides yet more evidence that the Riemann Hypothesis, if true, is just barely true.