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Écarts entre nombres premiers successifs

Emmanuel Kowalski (2005/2006)

Séminaire Bourbaki

Le théorème des nombres premiers dit que la distance entre deux nombres premiers consécutifs p n < p n + 1 est, en moyenne, de l’ordre de ln ( p n ) . Récemment, D. Goldston, J. Pintz et C. Yıldırım sont parvenus à démontrer que la distance normalisée ( p n + 1 - p n ) / ln ( p n ) pouvait devenir arbitrairement petite, améliorant spectaculairement les résultats connus auparavant. Sous des hypothèses considérées comme raisonnables, ils parviennent à montrer que p n + 1 - p n < 16 infiniment souvent. Leur méthode est une très jolie application d’idées inspirée par...

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