prime number theorem

[¦prīm ¦nəm·bər ‚thir·əm] (mathematics) The theorem that the limit of the quantity [π(x)] (ln x)/ x as x approaches infinity is 1, where π(x) is the number of prime numbers not greater than x and ln x is the natural logarithm of x.

prime number theorem

(mathematics)The number of prime numbers less than x isabout x/log(x). Here "is about" means that the ratio of thetwo things tends to 1 as x tends to infinity. This was firstconjectured by Gauss in the early 19th century, and wasproved (independently) by Hadamard and de la Vall'ee Poussinin 1896. Their proofs relied on complex analysis, but Erd?sand Selberg later found an "elementary" proof.

单词	prime number theorem
释义	prime number theorem prime number theorem [¦prīm ¦nəm·bər ‚thir·əm] (mathematics) The theorem that the limit of the quantity [π(x)] (ln x)/ x as x approaches infinity is 1, where π(x) is the number of prime numbers not greater than x and ln x is the natural logarithm of x. prime number theorem (mathematics)The number of prime numbers less than x isabout x/log(x). Here "is about" means that the ratio of thetwo things tends to 1 as x tends to infinity. This was firstconjectured by Gauss in the early 19th century, and wasproved (independently) by Hadamard and de la Vall'ee Poussinin 1896. Their proofs relied on complex analysis, but Erd?sand Selberg later found an "elementary" proof. AcronymsSeePNT
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