A new ceiling for Λ: the de Bruijn–Newman constant

Researchers have established a new upper bound of 0.178785 for the de Bruijn-Newman constant (Λ), a value that would determine whether the Riemann hypothesis is true. The Riemann hypothesis, one of mathematics' greatest unsolved problems, governs the distribution of prime numbers and the error term in counting primes; proving it would sharpen hundreds of results in number theory. The proof combines three finite computational checks—machine verification of the hypothesis below a certain threshold, certification of zero-free regions, and identification of a barrier—to establish this tighter bound on Λ.