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楼主 |
发表于 2019-1-26 11:13
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比如以今天日期乘以1000的连续偶数的素对数量的计算:
真值如下:
G(20190126000) = 77148293
G(20190126002) = 26538989
G(20190126004) = 25876781
G(20190126006) = 52108022
G(20190126008) = 28227624
使用素数连乘式的计算:
Sp( 20190126000 *) = 1/(1+ .1533 )*( 20190126000 /2 -2)*p(m) ≈ 77121815.9 , k(m)= 2.981448 ;Δ(m)≈-0.000343
Sp( 20190126002 *) = 1/(1+ .1533 )*( 20190126002 /2 -2)*p(m) ≈ 26525150.5 , k(m)= 1.025434 ;Δ(m)≈-0.000521
Sp( 20190126004 *) = 1/(1+ .1533 )*( 20190126004 /2 -2)*p(m) ≈ 25867231.1 , k(m)= 1; Δ(m)≈-0.000369
Sp( 20190126006 *) = 1/(1+ .1533 )*( 20190126006 /2 -2)*p(m) ≈ 52083461.5 , k(m)= 2.013492 ;Δ(m)≈-0.000471
Sp( 20190126008 *) = 1/(1+ .1533 )*( 20190126008 /2 -2)*p(m) ≈ 28218797.5 , k(m)= 1.090909; Δ(m)≈-0.000313;
start time =10:30:14,end time=10:31:59 ,
而采用对数式 Xi(M)=t2*c1*M/(logM)^2 计算,计算速度则比素数连乘式略微快一点:
S( 20190126000 ) = 77148293 ;Xi(M)≈ 77006797.26 δxi(M)≈-0.001834 ( t2= 1.091059 )
S( 20190126002 ) = 26538989 ;Xi(M)≈ 26485591.3 δxi(M)≈-0.002012 ( t2= 1.091059 )
S( 20190126004 ) = 25876781 ;Xi(M)≈ 25828653.33 δxi(M)≈-0.001860 ( t2= 1.091059 )
S( 20190126006 ) = 52108022 ;Xi(M)≈ 52005786.53 δxi(M)≈-0.001962 ( t2= 1.091059 )
S( 20190126008 ) = 28227624 ;Xi(M)≈ 28176712.31 δxi(M)≈-0.001804 ( t2= 1.091059 )
time start =10:38:53, time end =10:40:04
很明显,用这两个素对计算式的计算值的计算精度都比较高,相对误差绝对值都很小。
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