我们已经证明了3大倍增定理,我们是否还要继续验证下去?
实际上:x→∞时
limπ(N^(x+1))/π(N^x)
x→∞
=
lim(N^(x+1)/ln(N^(x+1)))/N^x/ln(N^x)
x→∞
=
Nlim(1+1/x)=N
x→∞
π(N^(x+1))/π(N^x)~N
奇素数定理:
π(N^(x+1))~N*π(N^x)
π(N^(x+1))/π(N^x)~N
我用老师们给我的大数据验证如下:
π(10^2)/π(10)=25/4=6.25
π(10^3)/π(10^2)=168/25≈6.7
π(10^4)/π(10^3)=1229/168≈7.3
π(10^5)/π(10^4)=9592/1229≈7.8
π(10^6)/π(10^5)=78948/9592≈8.2
π(10^7)/π(10^6)=664579/78948≈8.4
π(10^8)/π(10^7)=5761455 /664579≈8.6
π(10^9)/π(10^8)=50847534 /5761455 ≈8.8
π(10^10)/π(10^9)=455052511/50847534 ≈8.9
π(10^11)/π(10^10)=4118054813/455052511≈9.0
π(10^12)/π(10^11)=37607912018/4118054813≈9.1
π(10^13)/π(10^12)=346065536839/37607912018≈9.2
π(10^14)/π(10^13)=3204941750802/346065536839≈9.2
π(10^15)/π(10^14)=29844570422669/3204941750802≈9.3
π(10^16)/π(10^15)=279238341033925/29844570422669≈9.3
π(10^17)/π(10^16)=2623557157654233/279238341033925≈9.3
π(10^18)/π(10^17)=24739954287740860/2623557157654233≈9.4
π(10^19)/π(10^18)=234057667276344607/24739954287740860≈9.4
π(10^20)/π(10^19)=2220819602560918849/234057667276344607≈9.4
π(10^21)/π(10^20)=21127269486018731928/2220819602560918849≈9.5
π(10^22)/π(10^21)=201467286689315906290/21127269486018731928≈9.5
π(10^23)/π(10^22)=1925320391606803968923/201467286689315906290≈9.5
π(10^24)/π(10^23)=18435599767349200867866/1925320391606803968923≈9.5
π(10^25)/π(10^24)=176846309399143769411680/18435599767349200867866≈9.60
π(10^26)/π(10^25)=1699246750872437141327603/176846309399143769411680≈9.60
π(10^27)/π(10^26)=16352460426841680446427399/1699246750872437141327603≈9.62
π(10^28)/π(10^27)=157589269275973410412739598/16352460426841680446427399≈9.64
π(10^(x+1))/π(10^x)~10