连乘积公式计算哥猜数误差分析

重生888@ · 发表于 2022-8-1 02:23

本帖最后由重生888@ 于 2022-8-1 07:13 编辑

yangchuanju 发表于 2022-7-31 20:14
不知何故，吴先生在《特定偶数的哥猜数》中的两贴，有时显示在48、49楼，有时显示在49、50楼，楼号有变化 ...

谢谢杨先生关注！我的计算精度是一以贯之（大概在一年半内，两年前我没有斐波那切数列倒数和，计算精度差些。）
现在确定了F，不存在多大差别。是不是杨先生看了以往的帖子？谢谢！

重生888@ · 发表于 2022-8-1 11:02

G(12000000000) = 42963384             D（12000000000）=5/3（W）=42478548       D/G=0.988715
G(12000000002) = 16111595             D（12000000002）=5/8（W）=15929455       D/G=0.988695
G(12000000004) = 16115802             D（12000000004）=5/8（W）=15929455       D/G
G(12000000006) = 32219199             D（12000000006）=5/4（W）=31858911       D/G=0.988817
G(12000000008) = 16112912
G(12000000010) = 21510901             D（12000000010）=5/6（W）=21239274       D/G=0.987372
G(12000000012) = 49626854
G(12000000014) = 16105825
G(12000000016) = 16810315
G(12000000018) = 34696654
G(12000000020) = 21479143
G(12000000022) = 16146240
G(12000000024) = 33056247
G(12000000026) = 20048735
G(12000000028) = 16148508
G(12000000030) = 42969082
G(12000000032) = 16382094
G(12000000034) = 17913745
G(12000000036) = 33864037
G(12000000038) = 17693576

W=【N+F*N/lnN】/(lnN)^2                         F=3.341704

每一种组合最大下限值=42478548/4=10619637             计算值与真值比，精确度95/100以上！

愚工688 · 发表于 2022-8-1 13:04

本帖最后由愚工688 于 2022-8-1 05:31 编辑

愚工688 发表于 2022-7-31 07:14
对于需要控制在下界的偶数素对计算值，只需要把计算式中的修正系数(1/(1+t )的t 值略微的取大一些，就能 ...

200亿的连续偶数素数对下界数量的高精度计算：（可以比较180亿偶数的计算式的修正系数，仍然没有变化）

inf( 20000000000 )≈  34187864.9 , jd ≈0.99952 ,infS(m) = 25640898.64 , k(m)= 1.33333
inf( 20000000002 )≈  25908142.7 , jd ≈0.99963 ,infS(m) = 25640898.64 , k(m)= 1.01042
inf( 20000000004 )≈  51281797.3 , jd ≈0.99943 ,infS(m) = 25640898.64 , k(m)= 2
inf( 20000000006 )≈  30769078.4 , jd ≈0.99942 ,infS(m) = 25640898.65 , k(m)= 1.2
inf( 20000000008 )≈  25640898.7 , jd ≈0.99929 ,infS(m) = 25640898.65 , k(m)= 1
inf( 20000000010 )≈  68375729.8 , jd ≈0.99928 ,infS(m) = 25640898.65 , k(m)= 2.66667
inf( 20000000012 )≈  25815326.5 , jd ≈0.99934 ,infS(m) = 25640898.65 , k(m)= 1.0068
inf( 20000000014 )≈  26873618.8 , jd ≈0.99942 ,infS(m) = 25640898.66 , k(m)= 1.04808
inf( 20000000016 )≈  51770195.4 , jd ≈0.99941 ,infS(m) = 25640898.66 , k(m)= 2.01905
inf( 20000000018 )≈  25641655.3 , jd ≈0.99956 ,infS(m) = 25640898.66 , k(m)= 1.00003
inf( 20000000020 )≈  52653969.8 , jd ≈0.99924 ,infS(m) = 25640898.66 , k(m)= 2.05351
inf( 20000000022 )≈  51553129.6 , jd ≈0.99956 ,infS(m) = 25640898.67 , k(m)= 2.01058
time start =12:39:33  ,time end =12:43:58 ,time use =
计算式：
inf( 20000000000 ) = 1/(1+ .1535 )*( 20000000000 /2 -2)*p(m) ≈ 34187864.9
inf( 20000000002 ) = 1/(1+ .1535 )*( 20000000002 /2 -2)*p(m) ≈ 25908142.7
inf( 20000000004 ) = 1/(1+ .1535 )*( 20000000004 /2 -2)*p(m) ≈ 51281797.3
inf( 20000000006 ) = 1/(1+ .1535 )*( 20000000006 /2 -2)*p(m) ≈ 30769078.4
inf( 20000000008 ) = 1/(1+ .1535 )*( 20000000008 /2 -2)*p(m) ≈ 25640898.7
inf( 20000000010 ) = 1/(1+ .1535 )*( 20000000010 /2 -2)*p(m) ≈ 68375729.8
inf( 20000000012 ) = 1/(1+ .1535 )*( 20000000012 /2 -2)*p(m) ≈ 25815326.5
inf( 20000000014 ) = 1/(1+ .1535 )*( 20000000014 /2 -2)*p(m) ≈ 26873618.8
inf( 20000000016 ) = 1/(1+ .1535 )*( 20000000016 /2 -2)*p(m) ≈ 51770195.4
inf( 20000000018 ) = 1/(1+ .1535 )*( 20000000018 /2 -2)*p(m) ≈ 25641655.3
inf( 20000000020 ) = 1/(1+ .1535 )*( 20000000020 /2 -2)*p(m) ≈ 52653969.8
inf( 20000000022 ) = 1/(1+ .1535 )*( 20000000022 /2 -2)*p(m) ≈ 51553129.6

20000000000:13:2
偶数素数对真值：

G(20000000000) = 34204396
G(20000000002) = 25917735
G(20000000004) = 51311042
G(20000000006) = 30786908
G(20000000008) = 25659138
G(20000000010) = 68425196
G(20000000012) = 25832326
G(20000000014) = 26889096
G(20000000016) = 51800888
G(20000000018) = 25653066
G(20000000020) = 52694224
G(20000000022) = 51575932
G(20000000024) = 25668250

count = 13, algorithm = 2, working threads = 2, time use 8.404 sec

yangchuanju · 发表于 2023-11-21 08:15

本帖最后由 yangchuanju 于 2023-11-21 00:46 编辑

yangchuanju 发表于 2022-6-20 12:02
连乘积计算式筛分误差无规律且绝对值相当大
偶数单哥猜最大筛素累筛余累筛误差累乘余累乘误差 ...

原23楼贴数据有错误！
原23楼贴中的误差都是单计数据，而下面的误差是双计数据；双计误差约等于单计误差的2倍！

18480连乘积双计误差 18480连乘积单计误差
素数连乘积筛余误差连乘积筛余误差
3 6160 6160 0 3080 3080 0
5 4928 4928 0 2464 2464 0
7 4224 4224 0 2112 2112 0
11 3840 3840 0 1920 1920 0
13 3249.230769 3250 -0.769230769 1624.615385 1625 -0.384615385
17 2866.968326 2866 0.968325792 1433.484163 1433 0.484162896
19 2565.182186 2564 1.182186235 1282.591093 1282 0.591093117
23 2342.122866 2352 -9.877134307 1171.061433 1176 -4.938567154
29 2180.597151 2192 -11.40284918 1090.298575 1096 -5.701424591
31 2039.913464 2046 -6.086536332 1019.956732 1023 -3.043268166
37 1929.647871 1918 11.64787104 964.8239355 959 5.823935519
41 1835.518707 1804 31.5187066 917.7593533 902 15.7593533
43 1750.145743 1708 42.1457435 875.0728717 854 21.07287175
47 1675.671457 1632 43.67145654 837.8357283 816 21.83572827
53 1612.438571 1564 48.43857139 806.2192857 782 24.21928569
59 1557.779637 1506 51.77963677 778.8898184 753 25.88981838
61 1506.704895 1452 54.70489458 753.3524473 726 27.35244729
67 1461.728629 1396 65.72862907 730.8643145 698 32.86431453
71 1420.553175 1352 68.55317473 710.2765874 676 34.27658736
73 1381.63391 1314 67.63390967 690.8169548 657 33.81695483
79 1346.655836 1278 68.655836 673.327918 639 34.327918
83 1314.206298 1250 64.20629779 657.1031489 625 32.10314889
89 1284.673572 1220 64.67357199 642.336786 610 32.336786
97 1258.185457 1204 54.18545711 629.0927286 602 27.09272855
101 1233.270894 1184 49.2708936 616.6354468 592 24.6354468
103 1209.323886 1166 43.32388596 604.661943 583 21.66194298
107 1186.719701 1156 30.71970117 593.3598506 578 15.35985059
109 1164.945028 1136 28.94502776 582.4725139 568 14.47251388
113 1144.326532 1124 20.32653169 572.1632658 562 10.16326585
127 1126.305641 1118 8.305641428 563.1528207 559 4.152820714
131 1109.110135 1114 -4.889864548 554.5550677 557 -2.444932274

最小误差 -11.40284918 最小误差 -5.701424591
最大误差 68.655836 最大误差 34.327918

偶数18480的单哥571，双哥1142；
误差1=0，误差2=14*2=28，筛余1114+28=1142=双哥；
连乘积等于1109.11，综合误差-4.89；筛分过程中最大综合误差68.66，最小-11.40。
最大综合误差不超过131.

cuikun-186 · 发表于 2023-11-24 20:19

杨老师能否提供部分N内的孪生素数真值表？

cuikun-186 · 发表于 2023-11-26 15:14

cuikun-186 发表于 2023-11-24 12:19
杨老师能否提供部分N内的孪生素数真值表？

非常感谢杨老师提供的真值数据

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连乘积公式计算哥猜数误差分析

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