素数上下界估计之中值

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素数上下界估计之中值

中值估计是(上界估计+下界估计)/2

x=2^2
(2+2)/2=2
π(2^2)=2
2/2=1

x=2^3
(5.171 572 9+2.828 427 1)/2=4
π(2^3)=4
4/4=1

x=2^4
(9.650 396+6.349 604 2)/2=8
π(2^4)=6
8/6=1.333 333 333

x=2^5
(14.217 205 9+9.390 507 5)/2=11.803 856 7
π(2^5)=11
11.803 856 7/11=1.073 077 9

x=2^6
(25.393 258+17.769 336 9)/2=21.581 30
π(2^6)=18
21.581 30/18=1.198 961

x=2^7
(40.926 874+29.139 667)/2=35.033 27
π(2^7)=31
35.033 27/31=1.130 11


x=2^8
(69.535 45+50.630 634)/2=60.083 04
π(2^8)=54

x=2^9
(119.788 53+88.908 44)/2=104.3485
π(2^9)=97

x=2^10
(213.146 62+161.259 07)/2=187.2028
π(2^10)=172

x=2^11
(375.0477+287.7937)/2=331.4207
π(2^11)=309

x=2^12
(669.3301+520.3773)/2=594.8537
π(2^12)=564

x=2^13
(1214.673+956.207 98)/2=1085.44
π(2^13)=1028

x=2^14
(2203.028+1752.6084)/2=1977.818
π(2^14)=1900

x=2^15
(4053.92+3257.994)/2=3656.0
π(2^15)=3512

x=2^16
(7464.558+6052.3608)/2=6758.46
π(2^16)=6542

x=2^17
(13 856.96+11 329.023)/2=12 592.99
π(2^17)=12251

x=2^18
(25 869.78+21 313.37)/2=23 591.6
π(2^18)=23000

x=2^19
(48 433.80+40 183.34)/2=44 308.57
π(2^19)=43390

x=2^20
(91 143+76 113.69)/2=83 628.3
π(2^19)=82025