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Lexikon


prime number theorem


ematics> The number of ef="module.php?name=Lexikon&file=search&eid=1&query=prime number">prime numbers less than x is about x/log(x). Here "is about" means that the ratio of the two things tends to 1 as x tends to infinity. This was first conjectured by ef="module.php?name=Lexikon&file=search&eid=1&query=Gauss">Gauss in the early 19th century, and was proved (independently) by Hadamard and de la Vall' ee Poussin in 1896. Their proofs relied on ef="module.php?name=Lexikon&file=search&eid=1&query=complex analysis">complex analysis, but erdös and Selberg later found an "elementary" proof. (1995-04-10)

e="border-width:thin; border-color:#333333; border-style:dashed; padding:5px;" align="left">In addition suitable contents:
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