 By July of that year, Selberg and Paul Erdős had each obtained elementary proofs of the PNT, both using Selberg's asymptotic formula as a starting point.These proofs effectively laid to rest the notion that the PNT was "deep", and showed that technically "elementary" methods were more powerful than had been believed to be the case.On the history of the elementary proofs of the PNT, including the Erdős–Selberg priority dispute, see an article by Dorian Goldfeld.