Complex sentence: The distinction between elementary and non-elementary proofs is important in regard to the prime number theorem, which was first proved in 1896 by Jacques Hadamard and Charles Jean de la Vallée-Poussin using complex analysis.
Split into simpler sentences: The distinction between elementary and non-elementary proofs has been considered important in regard to the prime number theorem. It was first proved in 1896 by Jacques Hadamard and Charles Jean de la Vallée-Poussin using complex analysis.