The Elementary Proof of the Prime Number Theorem: An Historical Perspective
The Elementary Proof of the Prime Number Theorem: An Historical Perspective
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素数定理的基本证明：历史的视角
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发表时间：
2004
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影响因子：
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通讯作者：
D. Goldfeld
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文献类型：
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作者：
D. Goldfeld
The study of the distribution of prime numbers has fascinated mathematicians since antiquity. It is only in modern times, however, that a precise asymptotic law for the number of primes in arbitrarily long intervals has been obtained. For a real number x > 1, let π(x) denote the number of primes less than x. The prime number theorem is the assertion that
$$ mathop {lim }limits_{x o infty } pi left( x
ight){
aise0.7exhbox{${}$} !mathord{left/ {vphantom {{} {}}}
ight.kern-
ulldelimiterspace} !lower0.7exhbox{${}$}}frac{x} {{log (x)}} = 1. $$
This theorem was conjectured independently by Legendre and Gauss.
The study of the distribution of prime numbers has fascinated mathematicians since antiquity. It is only in modern times, however, that a precise asymptotic law for the number of primes in arbitrarily long intervals has been obtained. For a real number x > 1, let π(x) denote the number of primes less than x. The prime number theorem is the assertion that
$$ mathop {lim }limits_{x o infty } pi left( x
ight){
aise0.7exhbox{${}$} !mathord{left/ {vphantom {{} {}}}
ight.kern-
ulldelimiterspace} !lower0.7exhbox{${}$}}frac{x} {{log (x)}} = 1. $$
This theorem was conjectured independently by Legendre and Gauss.