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发表于 2016-2-26 22:26
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本帖最后由 愚工688 于 2016-2-26 15:02 编辑
对于几百万的偶数的素对的计算,相对误差就不能如同几十亿的偶数那样通过使用误差修正系数的方法做到那样小,因为在此范围内偶数素对计算值的相对误差分布的集中度还不是很高,因此相对误差统计计算的标准偏差不是很小,使用修正系数的效果不如大于亿的偶数。
样本的相对误差的统计计算:
[ 500002 , 500100 ] : n= 50 μ= .0536 σχ= .0084 δ(min)= .0359 δ(max)= .0698
[ 1000002 , 1000100 ] : n= 50 μ= .0691 σχ= .0069 δ(min)= .0508 δ(max)= .0879
[ 2000002 , 2000100 ] : n= 50 μ= .0804 σχ= .0063 δ(min)= .0641 δ(max)= .0951
[ 3000002 , 3000100 ] : n= 50 μ= .0825 σχ= .005 δ(min)= .0706 δ(max)= .0923
对比的大偶数的相对误差的统计计算数据例:
3000000000 - 3000000098 : n= 50 μ= .1431 σx= .0002 δ(min)= .1425 δ(max)= .1435
4000000000 - 4000000098 : n= 50 μ= .1449 σx= .0003 δ(min)= .1441 δ(max)= .1456
40000000002-40000000100 : n= 50 μ= .15614 σx= .00008 δ(min)= .1559 δ(max)= .15637
50000000002-50000000100 : n= 50 μ= .1571 σx= .0001 δ(min)= .1569 δ(max)= .1573
很明显,几百万区域偶数的标准偏差的值比几十亿、百亿区域大了10倍以上,故采用修正系数后的计算值的相对误差稍微的大了一点:
G(2016026) = 7336 , Sp( 2016026 *)≈ 7351.8 , Δ≈ 0.00215, k(m)= 1
G(2016028) = 8973 , Sp( 2016028 *)≈ 8934.6 , Δ≈-0.00428, k(m)= 1.2153
G(2016030) = 21423 ,Sp( 2016030 *)≈ 21606 , Δ≈ 0.00854, k(m)= 2.93888
G(2016032) = 7298 ,Sp( 2016032 *)≈ 7381.3 , Δ≈ 0.01141, k(m)= 1.00402
G(2016034) = 7372 , Sp( 2016034 *)≈ 7351.8 , Δ≈-0.00274, k(m)= 1
G(2016036) = 16475, Sp( 2016036 *)≈ 16337.4 ,Δ≈-0.00835, k(m)= 2.22222
G(2016038) = 7370 , Sp( 2016038 *)≈ 7364.6 , Δ≈-0.00073, k(m)= 1.00174
G(2016040) = 10813, Sp( 2016040 *)≈ 10693.6 ,Δ≈-0.01104, k(m)= 1.45455
G(2016042) = 18432 ,Sp( 2016042 *)≈ 18484.6 ,Δ≈ 0.00285, k(m)= 2.51429
G(2016044) = 7317 , Sp( 2016044 *)≈ 7351.8 , Δ≈ 0.00531, k(m)= 1
G(2016046) = 7433 , Sp( 2016046 *)≈ 7366.9 , Δ≈-0.00889, k(m)= 1.00204
G(2016048) = 14912, Sp( 2016048 *)≈ 14893 , Δ≈-0.00127, k(m)= 2.02574
G(2016050) = 9959 , Sp( 2016050 *)≈ 9983.7 , Δ≈ 0.00248, k(m)= 1.35799
G(2016052) = 8018 , Sp( 2016052 *)≈ 7996.3 , Δ≈-0.00271, k(m)= 1.08766
G(2016054) = 15217, Sp( 2016054 *)≈ 15210.8 ,Δ≈-0.00041, k(m)= 2.06897
G(2016056) = 9170 , Sp( 2016056 *)≈ 9140.6 , Δ≈-0.00321, k(m)= 1.2433
G(2016058) = 8192 , Sp( 2016058 *)≈ 8168.8 , Δ≈-0.00283, k(m)= 1.11111
G(2016060) = 19517, Sp( 2016060 *)≈ 19605.1 ,Δ≈ 0.00451, k(m)= 2.66667
G(2016062) = 7281 , Sp( 2016062 *)≈ 7351.9 , Δ≈ 0.00974, k(m)= 1
G(2016064) = 7954 , Sp( 2016064 *)≈ 7915.3 , Δ≈-0.00487, k(m)= 1.07664
G(2016066) = 15942 ,Sp( 2016066 *)≈ 16040.5 ,Δ≈ 0.00618, k(m)= 2.18182
G(2016068) = 7319 , Sp( 2016068 *)≈ 7351.9 , Δ≈ 0.00450, k(m)= 1
G(2016070) = 11917, Sp( 2016070 *)≈ 11942.8 ,Δ≈ 0.00216, k(m)= 1.62445
G(2016072) = 14789 ,Sp( 2016072 *)≈ 14703.9 ,Δ≈-0.00575, k(m)= 2
G(2016074) = 7403 , Sp( 2016074 *)≈ 7351.9 , Δ≈-0.00690, k(m)= 1
G(2016076) = 7400 , Sp( 2016076 *)≈ 7372.7 , Δ≈-0.00369, k(m)= 1.00283
G(2016078) = 14698 ,Sp( 2016078 *)≈ 14780.9 ,Δ≈ 0.00564, k(m)= 2.01047
G(2016080) = 11468 ,Sp( 2016080 *)≈ 11441.9 ,Δ≈-0.00384, k(m)= 1.5563
G(2016082) = 7413 , Sp( 2016082 *)≈ 7352 , Δ≈-0.00823, k(m)= 1
G(2016084) = 17582 ,Sp( 2016084 *)≈ 17644.8 ,Δ≈ 0.00357, k(m)= 2.4
G(2016086) = 7332 , Sp( 2016086 *)≈ 7352 , Δ≈ 0.00273, k(m)= 1
G(2016088) = 7675 , Sp( 2016088 *)≈ 7702.1 , Δ≈ 0.00353, k(m)= 1.04762
G(2016090) = 20953 ,Sp( 2016090 *)≈ 20919.5 ,Δ≈-0.00160, k(m)= 2.84542
G(2016092) = 8032 , Sp( 2016092 *)≈ 8108.5 , Δ≈ 0.00952, k(m)= 1.1029
G(2016094) = 7466 , Sp( 2016094 *)≈ 7422 , Δ≈-0.00589, k(m)= 1.00952
G(2016096) = 14727, Sp( 2016096 *)≈ 14704.1, Δ≈-0.00155, k(m)= 2
G(2016098) = 9698 , Sp( 2016098 *)≈ 9689.6 , Δ≈-0.00087, k(m)= 1.31794
G(2016100) = 9788 , Sp( 2016100 *)≈ 9802.7 , Δ≈ 0.00150, k(m)= 1.33333
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