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发表于 2018-6-20 19:47
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正如前面曾经说过的那样,本帖中用Sp( m *)=Sp( m )/(1+μ) 来计算150-250亿偶数的素对数量,使用的μ=0.1533;
Sp( 20180620000 *) = 1/(1+ .1533 )*( 20180620000 /2 -2)*p(m) ≈ 34902854.3 , Δ≈-0.000521;
Sp( 20180620002 *) = 1/(1+ .1533 )*( 20180620002 /2 -2)*p(m) ≈ 53494717.6 , Δ≈-0.000353;
Sp( 20180620004 *) = 1/(1+ .1533 )*( 20180620004 /2 -2)*p(m) ≈ 26518748.9 , Δ≈-0.000504;
Sp( 20180620006 *) = 1/(1+ .1533 )*( 20180620006 /2 -2)*p(m) ≈ 25900746.7 , Δ≈-0.000561;
Sp( 20180620008 *) = 1/(1+ .1533 )*( 20180620008 /2 -2)*p(m) ≈ 51711560.3 , Δ≈-0.000417;
若仍用μ=0.1533作修正系数对更大的如250亿以上偶数进行计算,则相对误差就会逐渐增大。
举例如下:
G(30000000000) = 99039834;Sp( 30000000000 *)≈ 99186811.2 , Δ≈0.001484, k(m)= 2.66667
G(30000000002) = 44569004;Sp( 30000000002 *)≈ 44634065.0 , Δ≈0.001460, k(m)= 1.2
G(30000000004) = 40697862;Sp( 30000000004 *)≈ 40760026.5 , Δ≈0.001527, k(m)= 1.09585
G(30000000006) = 74283345;Sp( 30000000006 *)≈ 74390108.4 , Δ≈0.001437, k(m)= 2
G(35000000000) = 68412556;Sp( 35000000000 *)≈ 68545889.9 , Δ≈0.001949, k(m)= 1.6
G(35000000002) = 48894586;Sp( 35000000002 *)≈ 48985300.8 , Δ≈0.001855, k(m)= 1.14342
G(35000000004) = 85531578;Sp( 35000000004 *)≈ 85692221.1 , Δ≈0.001878, k(m)= 2.00023
G(35000000006) = 42755368;Sp( 35000000006 *)≈ 42841910.7 , Δ≈0.002024, k(m)= 1.00002
G(40000000000) = 64411146; Sp( 40000000000 *)≈ 64570309.4 , Δ≈0.002471, k(m)= 1.33333
G(40000000002) = 102364420;Sp( 40000000002 *)≈ 102615953.8 , Δ≈0.002457, k(m)= 2.11895
G(40000000004) = 48813213; Sp( 40000000004 *)≈ 48932473.4 , Δ≈0.002443, k(m)= 1.01042
G(40000000006) = 48934047; Sp( 40000000006 *)≈ 49056663.6 , Δ≈0.002506, k(m)= 1.01299
计算式:
Sp( 30000000000 *) = 1/(1+ .1533 )*( 30000000000 /2 -2)*p(m) ≈ 99186811.2 , k(m)= 2.66667
Sp( 30000000002 *) = 1/(1+ .1533 )*( 30000000002 /2 -2)*p(m) ≈ 44634065 , k(m)= 1.2
Sp( 30000000004 *) = 1/(1+ .1533 )*( 30000000004 /2 -2)*p(m) ≈ 40760026.5 , k(m)= 1.09585
Sp( 30000000006 *) = 1/(1+ .1533 )*( 30000000006 /2 -2)*p(m) ≈ 74390108.40000001 , k(m)= 2
Sp( 35000000000 *) = 1/(1+ .1533 )*( 35000000000 /2 -2)*p(m) ≈ 68545889.90000001 , k(m)= 1.6
Sp( 35000000002 *) = 1/(1+ .1533 )*( 35000000002 /2 -2)*p(m) ≈ 48985300.8 , k(m)= 1.14342
Sp( 35000000004 *) = 1/(1+ .1533 )*( 35000000004 /2 -2)*p(m) ≈ 85692221.09999999 , k(m)= 2.00023
Sp( 35000000006 *) = 1/(1+ .1533 )*( 35000000006 /2 -2)*p(m) ≈ 42841910.7 , k(m)= 1.00002
Sp( 40000000000 *) = 1/(1+ .1533 )*( 40000000000 /2 -2)*p(m) ≈ 64570309.4 , k(m)= 1.33333
Sp( 40000000002 *) = 1/(1+ .1533 )*( 40000000002 /2 -2)*p(m) ≈ 102615953.8 , k(m)= 2.11895
Sp( 40000000004 *) = 1/(1+ .1533 )*( 40000000004 /2 -2)*p(m) ≈ 48932473.4 , k(m)= 1.01042
Sp( 40000000006 *) = 1/(1+ .1533 )*( 40000000006 /2 -2)*p(m) ≈ 49056663.6 , k(m)= 1.01299
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