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prime number theorem
(redirected from Distribution of prime numbers)

   Also found in: Wikipedia 0.01 sec.
prime number theorem [¦prīm ¦nəm·bər ‚thir·əm]
(mathematics)
The theorem that the limit of the quantity [π(x)] (lnx)/xasxapproaches infinity is 1, where π(x) is the number of prime numbers not greater thanxand lnxis the natural logarithm ofx.

(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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For example, Rockmore relies on Sir Michael Berry's "music of the primes" analogy--Sir Michael actually played the "music" at a 1996 conference--to explain the relevance of the RH to the distribution of prime numbers.
115 QA246 Euler, Dirichlet and Rieman pioneered work leading to the study of the analytic properties of L-functions as they relate to the distribution of prime numbers.
A mathematical duo has made a surprising advance in understanding the distribution of prime numbers, those whole numbers divisible only by themselves and 1.
 
 
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