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prime number theorem

   Also found in: Acronyms, Wikipedia 0.04 sec.
(mathematics)prime number theorem - The number of 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 Gauss in the early 19th century, and was proved (independently) by Hadamard and de la Vall'ee Poussin in 1896. Their proofs relied on complex analysis, but Erdös and Selberg later found an "elementary" proof.


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In the case of the prime number theorem, Gauss later refined his conjecture but never did figure out how to prove it.
Math lab: computer experiments are transforming mathematics by Klarreich, Erica / Science News
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