在100以内有多少个质数？1000、10000呢？

设 \pi(x) 为 素数计数函数，则我们有

\pi(10)=4,

\pi(10^2)=25,

\pi(10^3)=168,

\pi(10^4)=1229,

\pi(10^5)=9592,

\pi(10^6)=78498,

\pi(10^7)=664579,

\pi(10^8)=5761455,

\pi(10^9)=50847534,

\pi(10^{10})=455052511,

\pi(10^{11})=4118054813,

\pi(10^{12})=37607912018,

\pi(10^{13})=346065536839,

\pi(10^{14})=3204941750802,

\pi(10^{15})=29844570422669,

\pi(10^{16})=279238341033925,

\pi(10^{17})=2623557157654233,

\pi(10^{18})=24739954287740860,

\pi(10^{19})=234057667276344607,

\pi(10^{20})=2220819602560918840,

\pi(10^{21})=21127269486018731928,

\pi(10^{22})=201467286689315906290,

\pi(10^{23})=1925320391606803968923,

\pi(10^{24})=18435599767349200867866,

\pi(10^{25})=176846309399143769411680,

\pi(10^{26})=1699246750872437141327603,

\pi(10^{27})=16352460426841680446427399.