  The structure of a solvable Lie groups admitting an Einstein left-invariant
metric is, in a sense, completely determined by the nilradical of its Lie
algebra. We give an easy-to-check necessary and sufficient condition for a
nilpotent algebra to be an Einstein nilradical whose Einstein derivation has
simple eigenvalues. As an application, we classify filiform Einstein
nilradicals (modulo known classification results on filiform graded Lie
algebras).
