探索高精度计算素数对个数的弥合计算公式

愚工688 · 发表于 2023-3-16 10:37

从50亿开始：
G(50e8)=9703556;
G(51e8)=21074753;
G(52e8)=10965645;
G(53e8)=10432025;
G(54e8)=20806971;
G(55e8)=11751032;
G(56e8)=12902169;
G(57e8)=23138994;
G(58e8)=11513223;
G(59e8)=11470516;
G(60e8)=22899781;
G(61e8)=11818360;
G(62e8)=12198951;
G(63e8)=28716471;
G(64e8)=12138392;
G(65e8)=13427034;
G(66e8)=27736743;
G(67e8)=12850259;
G(68e8)=13679782;
G(69e8)=27222854;
G(70e8)=15799407；
G(71e8)=13531786；
G(72e8)=27011820；
G(73e8)=13870610；
G(74e8)=14241533；
G(75e8)=28031543；
G(76e8)= 15018224；
G(77e8)=19135150；
G(78e8)= 31686056；
G(79e8)=14883005；
G(80e8)= 14862150；
G(81e8)= 30063256；
G(82e8)=15586610；
G(83e8)= 15553036；
G(84e8)= 37285242；
G(85e8)=16751667；
G(86e8)=16258121；
G(87e8)=33262802；
G(88e8)=18008203；
G(89e8)=16557548；
G(90e8)=33076258；
G(91e8)=21870485；
G(92e8)=17675475；
G(93e8)=35257514；
G(94e8)=17590961；
G(95e8)=18395699；
G(96e8)=35075543；
G(97e8)=17886783；
G(98e8)=21437787；
G(99e8)=40070955；
G(1e10)=18200488；

愚工688 · 发表于 2023-3-16 11:15

本帖最后由愚工688 于 2023-3-16 08:23 编辑

G（21e8）=10629971；
G（22e8）=5134372；
G（23e8）=5039234；
G（24e8）=9992839；
G（25e8）=5185533；
G（26e8）=5859790；
G（27e8）=11116031；
G（28e8）=6894453；
G（29e8）=6148656；
G（30e8）=12224533；
G（31e8）=6511564；
G（32e8）=6478775；
G（33e8）=14804731；
G（34e8）=7299554；
G（35e8）=8434100；
G（36e8）=14415400；
G（37e8）=7599208；
G（38e8）=8012125；
G（39e8）=16906288；
G（40e8）=7930427；
G（41e8）=8314407；
G（42e8）=19883421；
G（43e8）=8667672；
G（44e8）=9603218；
G（45e8）=17642968；
G（46e8）=9425212；
G（47e8）=9378444；
G（48e8）=18704238；
G（49e8）=11434201；

不是连续的偶数，要手工记录筛选程序的素数对数量，再输入到页面上，容易出错。眼一花，手一抖，都会产生错误。只有拷贝程序生成的数据才没有错误。

愚工688 · 发表于 2023-3-16 12:01

本帖最后由愚工688 于 2023-3-16 04:32 编辑

Xi(M)=t2*c1*M/(logM)^2

  G( 1100000000 ) = ?    ;Xi(M)≈ 2750206.71       jd(m)≈ ?1.00059;

  G( 1200000000 ) = ?    ;Xi(M)≈ 5353022.26       jd(m)≈ ?1.00018;

  G( 1300000000 ) =       ;Xi(M)≈ 3137707.54       jd(m)≈ ?1.00015;

  G( 1400000000 ) = ?    ;Xi(M)≈ 3689386.22       jd(m)≈ ?1.00034;

  G( 1500000000 ) = ?    ;Xi(M)≈ 6542800.45       jd(m)≈ ?0.99988;

  G( 1600000000 ) = ?    ;Xi(M)≈ 3467067.91       jd(m)≈ ?0.99990;

  G( 1700000000 ) = ?    ;Xi(M)≈ 3905685.14       jd(m)≈ ? 1.00032;

  G( 1800000000 ) = ?    ;Xi(M)≈ 7710027.35       jd(m)≈ ? 1.00010;

  G( 1900000000 ) = ?    ;Xi(M)≈ 4285521.41       jd(m)≈ ? 1.00013;

  G( 2000000000 ) = ?    ;Xi(M)≈ 4238910.11       jd(m)≈ ? 1.00012;

  G( 2100000000 ) = ?    ;Xi(M)≈ 10630768.05    jd(m)≈ ? 1.00007;

  G( 2200000000 ) = ?    ;Xi(M)≈ 5132462.02       jd(m)≈ ? 0.99963;

  G( 2300000000 ) = ?    ;Xi(M)≈ 5037099.2       jd(m)≈ ? 0.99958;

  G( 2400000000 ) = ?    ;Xi(M)≈ 9992600.02       jd(m)≈ ? 0.99998;

  G( 2500000000 ) = ?    ;Xi(M)≈ 5183731.18       jd(m)≈ ? 0.99965;
  time start =11:38:38, time end =11:38:41
  G( 2600000000 ) = ?    ;Xi(M)≈ 5858690.98       jd(m)≈ ? 0.99981;
  time start =11:38:46, time end =11:38:50
  G( 2700000000 ) = ?    ;Xi(M)≈ 11113074.52    jd(m)≈ ? 0.99973;
  time start =11:38:55, time end =11:38:59
  G( 2800000000 ) = ?    ;Xi(M)≈ 6890364.04       jd(m)≈ ? 0.99941;
  time start =11:39:03, time end =11:39:06
  G( 2900000000 ) = ?    ;Xi(M)≈ 6146302.32       jd(m)≈ ? 0.99962;
  time start =11:39:12, time end =11:39:16
  G( 3000000000 ) = ?    ;Xi(M)≈ 12222049.53    jd(m)≈ ? 0.99980;
  time start =11:39:21, time end =11:39:25

从上面的时间记录可以看出，一个偶数的素对计算在0.03~0.04分钟，即1.8~2.4秒。Basic 程序在计算速度上面还是可以的。

yangchuanju · 发表于 2023-3-16 12:18

本帖最后由 yangchuanju 于 2023-3-18 08:49 编辑

单计1-100亿的素数对数表：
亿素数对
1 291400
2 538290
3 1547388
4 999700
5 1219610
6 2874881
7 1979689
8 1859646
9 4132595
10 2274205
11 2748595
12 5352052
13 3137228
14 3688114
15 6543613
16 3467407
17 3904453
18 7709245
19 4284979
20 4238417
21 10629971
22 5134372
23 5039234
24 9992839
25 5185533
26 5859790
27 11116031
28 6894453
29 6148656
30 12224533
31 6511564
32 6478775
33 14804731
34 7299554
35 8434100
36 14415400
37 7599208
38 8012125
39 16906288
40 7930427
41 8314407
42 19883421
43 8667672
44 9603218
45 17642968
46 9425212
47 9378444
48 18704238
49 11434201
50 9703556
51 21074753
52 10965645
53 10432025
54 20806971
55 11751032
56 12902169
57 23138994
58 11513223
59 11470516
60 22899781
61 11818360
62 12198951
63 28716471
64 12138392
65 13427034
66 27736743
67 12850259
68 13679782
69 27222854
70 15799407
71 13531786
72 27011820
73 13870610
74 14241533
75 28031543
76 15018224
77 19135150
78 31686056
79 14883005
80 14862150
81 30063256
82 15586610
83 15553036
84 37285242
85 16751667
86 16258121
87 33262802
88 18008203
89 16557548
90 33076258
91 21870485
92 17675475
93 35257514
94 17590961
95 18395699
96 35075543
97 17886783
98 21437787
99 40070955
100 18200488
表中32亿的素数对愚公老师提供数据是64478775，多了一位，改为6478775；
20亿的素数对那宝吉来说提供数据是4238418，比愚公老师早年提供的数据4238417多了1，1999999999不是素数（含素因子31），
请两位老师复核。

经用我的程序花费一个多小时的时间复核，20亿的素数对为4238417，上面的数据表已改正。

yangchuanju · 发表于 2023-3-16 12:21

重生、愚公、那宝吉计算式对比3（偶数10^8--10^10）:
求1,2,3……100*10^8共100个偶数的单计素数对，当采用哈李计算式时主项为0.660161816*N/ln(N)^2*波动系数，因偶数为有限的，主项（计算值）小于真实值；
11-100亿的真实素数对数分别由那宝吉、愚公两位老师提供，对于上述偶数，重生、愚公、那宝吉三人所用波动系数不完全一样，为便于比较调整为相同的波动系数，并单独列出；
重生计算值是在在N/ln(N)^2前乘以（1+F/ln(N)，再乘以0.625*波动系数，
愚公计算值是在N/ln(N)^2前乘以t2=1.358-ln(N)^(0.5)*.05484，再乘以0.660161816*波动系数，
那宝吉计算值是在N/ln(N)^2前乘以DT=(1/ln(WS+1)^(1/2.7289))*(1-ln(N)^2/(N*FL))，再乘以波动系数（分类系数）；
下面分别计算如下：
偶数波动系数 N/ln(N)^2 重生F （1+F/ln(N) 重生计算值
100000000 1.333333 294705.7766 3.282875 1.178217 289356.0899
200000000 1.333333 547437.6364 3.282875 1.171754 534551.8443
300000000 2.666667 787395.7871 3.282875 1.168186 1533041.47
400000000 1.333333 1019585.569 3.282875 1.165743 990479.2923
500000000 1.333333 1246243.655 3.282875 1.163897 1208749.33
600000000 2.666667 1468634.594 3.282875 1.162419 2845280.185
700000000 1.600000 1687568.307 3.282875 1.161189 1959586.172
800000000 1.333333 1903606.082 3.282875 1.160139 1840373.54
900000000 2.666667 2117158.768 3.282875 1.159224 4090437.155
1000000000 1.333333 2328539.469 3.312287 1.159834 2250599.817
1100000000 1.481481 2537994.309 3.312287 1.159102 2723884.737
1200000000 2.666667 2745721.578 3.312287 1.158440 5301257.479
1300000000 1.454545 2951884.259 3.312287 1.157836 3107088.878
1400000000 1.600000 3156618.554 3.312287 1.157281 3653093.261
1500000000 2.666667 3360039.891 3.312287 1.156767 6477971.964
1600000000 1.333333 3562247.271 3.312287 1.156290 3432491.173
1700000000 1.422222 3763326.488 3.312287 1.155844 3866504.46
1800000000 2.666667 3963352.563 3.312287 1.155426 7632266.294
1900000000 1.411765 4162391.628 3.312287 1.155032 4242086.004
2000000000 1.333333 4360502.385 3.312287 1.154661 4195752.275
2100000000 3.200000 4557737.276 3.312287 1.154310 10522079.91
2200000000 1.481481 4754143.418 3.312287 1.153976 5079784.252
2300000000 1.396825 4949763.357 3.312287 1.153658 4985214.007
2400000000 2.666667 5144635.696 3.312287 1.153356 9889324.112
2500000000 1.333333 5338795.608 3.312287 1.153066 5129987.823
2600000000 1.454545 5532275.263 3.312287 1.152789 5797771.13
2700000000 2.666667 5725104.197 3.312287 1.152524 10997198.7
2800000000 1.600000 5917309.611 3.312287 1.152269 6818331.649
2900000000 1.382716 6108916.635 3.312287 1.152024 6081890.628
3000000000 2.666667 6299948.552 3.312287 1.151787 12093669.46
3100000000 1.379310 6490426.992 3.312287 1.151560 6443201.94
3200000000 1.333333 6680372.095 3.312287 1.151340 6409482.225
3300000000 2.962963 6869802.662 3.312287 1.151127 14644477.65
3400000000 1.422222 7058736.278 3.312287 1.150922 7221380.927
3500000000 1.600000 7247189.426 3.312287 1.150723 8339505.656
3600000000 2.666667 7435177.587 3.312287 1.150530 14257321.99
3700000000 1.371429 7622715.323 3.312287 1.150343 7516057.676
3800000000 1.411765 7809816.358 3.312287 1.150161 7925774.742
3900000000 2.909091 7996493.649 3.312287 1.149984 16719711.41
4000000000 1.333333 8182759.442 3.312287 1.149812 7840532.186
4100000000 1.367521 8368625.332 3.312287 1.149645 8223034.959
4200000000 3.200000 8554102.311 3.312287 1.149483 19665583.07
4300000000 1.365854 8739200.814 3.312287 1.149324 8574294.241
4400000000 1.481481 8923930.758 3.312287 1.149169 9495470.526
4500000000 2.666667 9108301.582 3.312287 1.149019 17442679.65
4600000000 1.396825 9292322.275 3.312287 1.148871 9320040.79
4700000000 1.362963 9476001.413 3.312287 1.148728 9272700.887
4800000000 2.666667 9659347.18 3.312287 1.148587 18491003.45
4900000000 1.600000 9842367.401 3.312287 1.148450 11303465.27
5000000000 1.333333 10025069.56 3.312287 1.148316 9593286.044
5100000000 2.844444 10207460.81 3.312287 1.148184 20835635.1
5200000000 1.454545 10389548.03 3.312287 1.148056 10843434.64
5300000000 1.359477 10571337.79 3.312287 1.147930 10310912.93
5400000000 2.666667 10752836.42 3.312287 1.147806 20570287.05
5500000000 1.481481 10934049.99 3.312287 1.147685 11619303.78
5600000000 1.600000 11114984.33 3.312287 1.147567 12755186.03
5700000000 2.823529 11295645.05 3.312287 1.147450 22872693.37
5800000000 1.382716 11476037.56 3.312287 1.147336 11378781.12
5900000000 1.356725 11656167.06 3.312287 1.147224 11339033.53
6000000000 2.666667 11836038.56 3.312287 1.147115 22628819.57
6100000000 1.355932 12015656.92 3.312287 1.147007 11679693.04
6200000000 1.379310 12195026.79 3.312287 1.146901 12057313.24
6300000000 3.200000 12374152.69 3.312287 1.146796 28381267.9
6400000000 1.333333 12553038.98 3.312287 1.146694 11995412.38
6500000000 1.454545 12731689.86 3.312287 1.146593 13270973.83
6600000000 2.962963 12910109.41 3.312287 1.146494 27409940.68
6700000000 1.353846 13088301.58 3.312287 1.146397 12696022.24
6800000000 1.422222 13266270.18 3.312287 1.146301 13517459.3
6900000000 2.793651 13444018.91 3.312287 1.146207 26905699.39
7000000000 1.600000 13621551.35 3.312287 1.146114 15611852.65
7100000000 1.352657 13798870.99 3.312287 1.146023 13369171.83
7200000000 2.666667 13975981.18 3.312287 1.145933 26692558.58
7300000000 1.352113 14152885.21 3.312287 1.145844 13704507.8
7400000000 1.371429 14329586.24 3.312287 1.145757 14072761.29
7500000000 2.666667 14506087.37 3.312287 1.145671 27698667.84
7600000000 1.411765 14682391.58 3.312287 1.145586 14841125.42
7700000000 1.777778 14858501.8 3.312287 1.145502 18911610.42
7800000000 2.909091 15034420.85 3.312287 1.145420 31310410.59
7900000000 1.350649 15210151.5 3.312287 1.145339 14705848.9
8000000000 1.333333 15385696.41 3.312287 1.145259 14683833.08
8100000000 2.666667 15561058.21 3.312287 1.145179 29700339.24
8200000000 1.367521 15736239.43 3.312287 1.145101 15401358.53
8300000000 1.349794 15911242.55 3.312287 1.145024 15369736.22
8400000000 3.200000 16086069.97 3.312287 1.144948 36835439.06
8500000000 1.422222 16260724.06 3.312287 1.144873 16547972.83
8600000000 1.365854 16435207.1 3.312287 1.144799 16061596.46
8700000000 2.765432 16609521.33 3.312287 1.144726 32862585.29
8800000000 1.481481 16783668.93 3.312287 1.144654 17788418.39
8900000000 1.348659 16957652.02 3.312287 1.144583 16360441.1
9000000000 2.666667 17131472.68 3.312287 1.144512 32678628.4
9100000000 1.745455 17305132.95 3.312287 1.144442 21605158.11
9200000000 1.396825 17478634.79 3.312287 1.144374 17462140.73
9300000000 2.758621 17651980.15 3.312287 1.144306 34826310.36
9400000000 1.362963 17825170.92 3.312287 1.144238 17374579.21
9500000000 1.411765 17998208.94 3.312287 1.144172 18170334.86
9600000000 2.666667 18171096.03 3.312287 1.144106 34649442.07
9700000000 1.347368 18343833.93 3.312287 1.144041 17672509.05
9800000000 1.600000 18516424.39 3.312287 1.143977 21182366.05
9900000000 2.962963 18688869.1 3.312287 1.143914 39589725.81
10000000000 1.333333 18861169.7 3.330469 1.144640 17991047.87

yangchuanju · 发表于 2023-3-16 12:22

（接上楼）
偶数愚公t2 愚公计算值那宝吉DT 那宝吉计算值哈李计算值
100000000 1.122630 291215.5777 0.736658 289462.9996 259404.6675
200000000 1.118243 538840.1901 0.736658 537699.4247 481863.2323
300000000 1.115713 1546553.147 0.736659 1546779.439 1386156.354
400000000 1.113934 999706.334 0.736659 1001449.088 897455.281
500000000 1.112563 1220441.292 0.736659 1224075.523 1096963.3
600000000 1.111449 2873574.195 0.736659 2885022.161 2585430.614
700000000 1.110511 1979495.184 0.736659 1989060.352 1782509.053
800000000 1.109701 1859396.639 0.736659 1869745.202 1675584.064
900000000 1.108988 4133324.794 0.736659 4158999.433 3727113.006
1000000000 1.108353 2271699.063 0.725791 2253378.632 2049617.126
1100000000 1.107779 2749733.347 0.725791 2728969.783 2482202.862
1200000000 1.107257 5352098.607 0.725792 5314190.774 4833654.782
1300000000 1.106778 3137165.017 0.725791 3116294.497 2834503.67
1400000000 1.106334 3688747.162 0.725792 3665675.128 3334206.459
1500000000 1.105922 6541664.167 0.725792 6503169.722 5915120.097
1600000000 1.105538 3466464.699 0.725792 3447265.071 3135546.17
1700000000 1.105177 3905004.77 0.725792 3884644.202 3533375.215
1800000000 1.104837 7708681.951 0.725792 7670847.866 6977210.735
1900000000 1.104516 4284772.55 0.725792 4264981.553 3879320.493
2000000000 1.104212 4238168.22 0.725792 4219754.272 3838182.897
2100000000 1.103923 10628905.4 0.725792 10585495.87 9628301.175
2200000000 1.103648 5131561.204 0.725792 5111877.239 4649635.485
2300000000 1.103385 5036214.217 0.725792 5018090.246 4564329.198
2400000000 1.103134 9990842.218 0.725792 9957155.71 9056778.784
2500000000 1.102893 5182818.33 0.725792 5166470.35 4699292.005
2600000000 1.102662 5857658.24 0.725792 5840405.422 5312286.377
2700000000 1.102440 11111113.14 0.725792 11080620.23 10078653.82
2800000000 1.102226 6889146.936 0.725792 6871573.584 6250210.974
2900000000 1.102020 6145215.425 0.725792 6130686.694 5576318.913
3000000000 1.101821 12219886.88 0.725792 12193199.53 11090627.94
3100000000 1.101629 6510597.86 0.725792 6497513.422 5909975.269
3200000000 1.101442 6476667.569 0.725792 6464743.712 5880168.765
3300000000 1.101262 14798292.48 0.725792 14773467.28 13437574.52
3400000000 1.101087 7297373.969 0.725792 7286288.192 6627424.938
3500000000 1.100918 8427424.675 0.725792 8415918.663 7654908.372
3600000000 1.100753 14407889.75 0.725792 14390372.22 13089120.9
3700000000 1.100593 7595563.837 0.725792 7587432.207 6901337.952
3800000000 1.100437 8009747.137 0.725792 8002304.522 7278695.364
3900000000 1.100286 16897121.11 0.725792 16883747.26 15357032.06
4000000000 1.100138 7923846.467 0.725792 7918637.313 7202593.778
4100000000 1.099994 8310534.287 0.725792 8306157.827 7555072.679
4200000000 1.099854 19875116.37 0.725792 19867186.75 18070693.49
4300000000 1.099717 8665767.623 0.725792 8663389.175 7880001.319
4400000000 1.099583 9596894.542 0.725792 9595428.143 8727760.497
4500000000 1.099452 17629207.89 0.725792 17628610.72 16034541.1
4600000000 1.099324 9419819.192 0.725792 9420594.796 8568736.486
4700000000 1.099199 9372079.673 0.725792 9373917.112 8526279.64
4800000000 1.099077 18689383.95 0.725792 18695128.85 17004619.14
4900000000 1.098957 11424855.71 0.725792 11429612.3 10396088.22
5000000000 1.098840 9696409.811 0.725792 9701481.725 8824224.165
5100000000 1.098725 21059817.53 0.725792 21073037.18 19167504.68
5200000000 1.098612 10960209.91 0.725792 10968213.49 9976411.482
5300000000 1.098502 10422049.43 0.725792 10430708.19 9487510.193
5400000000 1.098394 20792189.74 0.725792 20811516.5 18929632.06
5500000000 1.098287 11744748.56 0.725792 11756802.61 10693692.29
5600000000 1.098183 12893001.45 0.725792 12907459.89 11740301.18
5700000000 1.098081 23120011.32 0.725792 23148097.9 21054927.67
5800000000 1.097980 11501907.38 0.725792 11516934.81 10475514.58
5900000000 1.097881 11461816.26 0.725792 11477824.54 10439940.86
6000000000 1.097784 22874019.13 0.725792 22907994.03 20836535.23
6100000000 1.097689 11806334.63 0.725792 11824898.99 10755631.04
6200000000 1.097595 12188133.09 0.725792 12208342.3 11104401.43
6300000000 1.097502 28689391.12 0.725792 28739380.97 26140617.96
6400000000 1.097412 12125719.79 0.725792 12147853.88 11049382.68
6500000000 1.097322 13415221.91 0.725792 13440805.49 12225418.91
6600000000 1.097234 27708040.07 0.725792 27763109.48 25252626
6700000000 1.097147 12834174.85 0.725792 12860698.46 11697768.16
6800000000 1.097062 13664628.81 0.725792 13693934.5 12455658.68
6900000000 1.096978 27198783.11 0.725792 27259205.44 24794287.57
7000000000 1.096895 15781997.95 0.725792 15818252.58 14387884.92
7100000000 1.096813 13514946.43 0.725792 13547001.79 12322012.39
7200000000 1.096733 26983746.49 0.725792 27049734.02 24603757.64
7300000000 1.096653 13854078.51 0.725792 13888962.88 12633051.58
7400000000 1.096575 14226419.85 0.725792 14263259.8 12973502.64
7500000000 1.096498 28001237.43 0.725792 28075725.08 25536973.28
7600000000 1.096422 15003312.77 0.725792 15044268.41 13683888.41
7700000000 1.096347 19118366.02 0.725792 19171868.84 17438249.83
7800000000 1.096272 31652856 0.725792 31743583.9 28873165.3
7900000000 1.096199 14866751.01 0.725792 14910359.13 13562087.9
8000000000 1.096127 14844555.19 0.725792 14889079.39 13542732.38
8100000000 1.096056 30025544.61 0.725792 30117562.51 27394177.19
8200000000 1.095985 15570057.01 0.725792 15618777.09 14206447.04
8300000000 1.095916 15538147.16 0.725792 15587756.65 14178231.63
8400000000 1.095847 37239193.65 0.725792 37360432.46 33982109.33
8500000000 1.095779 16729415.86 0.725792 16784920.66 15267141.87
8600000000 1.095712 16237763.36 0.725792 16292634.06 14819370.37
8700000000 1.095646 33223142.21 0.725792 33337427.02 30322884.88
8800000000 1.095580 17983646.53 0.725792 18046587.23 16414722.01
8900000000 1.095516 16540050.74 0.725792 16598919.83 15097960.2
9000000000 1.095452 33037488.11 0.725792 33157012.43 30158784.31
9100000000 1.095388 21842481.94 0.725792 21922770.66 19940400.86
9200000000 1.095326 17654008.18 0.725792 17719912.96 16117587.32
9300000000 1.095264 35209071.77 0.725792 35342509.38 32146657.31
9400000000 1.095203 17565586.04 0.725792 17633142.24 16038662.86
9500000000 1.095142 18370140.9 0.725792 18441810.87 16774207.48
9600000000 1.095082 35030551.96 0.725792 35169145.63 31988970
9700000000 1.095023 17866936.59 0.725792 17938595.13 16316495.12
9800000000 1.094964 21415463.22 0.725792 21502505.4 19558138.17
9900000000 1.094906 40025483.87 0.725792 40190296.34 36556082.26
10000000000 1.094849 18176569.54 0.716373 18015517.7 16601898.72

yangchuanju · 发表于 2023-3-16 12:23

本帖最后由 yangchuanju 于 2023-3-18 08:50 编辑

（接上楼）
偶数真实素数对重生/真实值愚公/真实值那宝吉/真实值哈李/真实值
100000000 291400 0.992986 0.999367 0.993353 0.890201
200000000 538290 0.993055 1.001022 0.998903 0.895174
300000000 1547388 0.990729 0.999460 0.999607 0.895804
400000000 999700 0.990777 1.000006 1.001750 0.897725
500000000 1219610 0.991095 1.000682 1.003661 0.899438
600000000 2874881 0.989704 0.999545 1.003528 0.899317
700000000 1979689 0.989845 0.999902 1.004734 0.900399
800000000 1859646 0.989636 0.999866 1.005431 0.901023
900000000 4132595 0.989799 1.000177 1.006389 0.901882
1000000000 2274205 0.989620 0.998898 0.990842 0.901246
1100000000 2748595 0.991010 1.000414 0.992860 0.903081
1200000000 5352052 0.990509 1.000009 0.992926 0.903140
1300000000 3137228 0.990393 0.999980 0.993327 0.903506
1400000000 3688114 0.990504 1.000172 0.993916 0.904041
1500000000 6543613 0.989969 0.999702 0.993819 0.903953
1600000000 3467407 0.989930 0.999728 0.994191 0.904291
1700000000 3904453 0.990281 1.000141 0.994927 0.904960
1800000000 7709245 0.990015 0.999927 0.995019 0.905045
1900000000 4284979 0.989990 0.999952 0.995333 0.905330
2000000000 4238417 0.989934 0.999941 0.995597 0.905570
2100000000 10629971 0.989850 0.999900 0.995816 0.905769
2200000000 5134372 0.989368 0.999453 0.995619 0.905590
2300000000 5039234 0.989280 0.999401 0.995804 0.905759
2400000000 9992839 0.989641 0.999800 0.996429 0.906327
2500000000 5185533 0.989288 0.999476 0.996324 0.906231
2600000000 5859790 0.989416 0.999636 0.996692 0.906566
2700000000 11116031 0.989310 0.999558 0.996814 0.906677
2800000000 6894453 0.988959 0.999230 0.996681 0.906556
2900000000 6148656 0.989141 0.999440 0.997078 0.906917
3000000000 12224533 0.989295 0.999620 0.997437 0.907243
3100000000 6511564 0.989501 0.999852 0.997842 0.907612
3200000000 6478775 0.989305 0.999675 0.997834 0.907605
3300000000 14804731 0.989176 0.999565 0.997888 0.907654
3400000000 7299554 0.989291 0.999701 0.998183 0.907922
3500000000 8434100 0.988784 0.999209 0.997844 0.907614
3600000000 14415400 0.989034 0.999479 0.998264 0.907996
3700000000 7599208 0.989058 0.999520 0.998450 0.908165
3800000000 8012125 0.989223 0.999703 0.998774 0.908460
3900000000 16906288 0.988964 0.999458 0.998667 0.908362
4000000000 7930427 0.988665 0.999170 0.998513 0.908223
4100000000 8314407 0.989010 0.999534 0.999008 0.908672
4200000000 19883421 0.989044 0.999582 0.999184 0.908832
4300000000 8667672 0.989227 0.999780 0.999506 0.909125
4400000000 9603218 0.988780 0.999342 0.999189 0.908837
4500000000 17642968 0.988648 0.999220 0.999186 0.908835
4600000000 9425212 0.988842 0.999428 0.999510 0.909129
4700000000 9378444 0.988725 0.999321 0.999517 0.909136
4800000000 18704238 0.988600 0.999206 0.999513 0.909132
4900000000 11434201 0.988566 0.999183 0.999599 0.909210
5000000000 9703556 0.988636 0.999264 0.999786 0.909380
5100000000 21074753 0.988654 0.999291 0.999919 0.909501
5200000000 10965645 0.988855 0.999504 1.000234 0.909788
5300000000 10432025 0.988390 0.999044 0.999874 0.909460
5400000000 20806971 0.988625 0.999290 1.000218 0.909774
5500000000 11751032 0.988790 0.999465 1.000491 0.910022
5600000000 12902169 0.988608 0.999289 1.000410 0.909948
5700000000 23138994 0.988491 0.999180 1.000393 0.909933
5800000000 11513223 0.988323 0.999017 1.000322 0.909868
5900000000 11470516 0.988537 0.999242 1.000637 0.910154
6000000000 22899781 0.988168 0.998875 1.000359 0.909901
6100000000 11818360 0.988267 0.998982 1.000553 0.910078
6200000000 12198951 0.988389 0.999113 1.000770 0.910275
6300000000 28716471 0.988327 0.999057 1.000798 0.910301
6400000000 12138392 0.988221 0.998956 1.000780 0.910284
6500000000 13427034 0.988377 0.999120 1.001026 0.910508
6600000000 27736743 0.988218 0.998965 1.000951 0.910439
6700000000 12850259 0.987997 0.998748 1.000812 0.910314
6800000000 13679782 0.988134 0.998892 1.001035 0.910516
6900000000 27222854 0.988350 0.999116 1.001335 0.910789
7000000000 15799407 0.988129 0.998898 1.001193 0.910660
7100000000 13531786 0.987983 0.998756 1.001124 0.910598
7200000000 27011820 0.988181 0.998961 1.001404 0.910852
7300000000 13870610 0.988025 0.998808 1.001323 0.910778
7400000000 14241533 0.988149 0.998939 1.001526 0.910963
7500000000 28031543 0.988125 0.998919 1.001576 0.911008
7600000000 15018224 0.988208 0.999007 1.001734 0.911152
7700000000 19135150 0.988318 0.999123 1.001919 0.911320
7800000000 31686056 0.988145 0.998952 1.001816 0.911226
7900000000 14883005 0.988097 0.998908 1.001838 0.911247
8000000000 14862150 0.988002 0.998816 1.001812 0.911223
8100000000 30063256 0.987928 0.998746 1.001806 0.911218
8200000000 15586610 0.988115 0.998938 1.002064 0.911452
8300000000 15553036 0.988215 0.999043 1.002232 0.911605
8400000000 37285242 0.987936 0.998765 1.002017 0.911409
8500000000 16751667 0.987840 0.998672 1.001985 0.911380
8600000000 16258121 0.987912 0.998748 1.002123 0.911506
8700000000 33262802 0.987968 0.998808 1.002243 0.911615
8800000000 18008203 0.987795 0.998636 1.002131 0.911514
8900000000 16557548 0.988096 0.998943 1.002499 0.911848
9000000000 33076258 0.987978 0.998828 1.002441 0.911796
9100000000 21870485 0.987868 0.998720 1.002391 0.911749
9200000000 17675475 0.987930 0.998786 1.002514 0.911862
9300000000 35257514 0.987770 0.998626 1.002411 0.911768
9400000000 17590961 0.987699 0.998558 1.002398 0.911756
9500000000 18395699 0.987749 0.998611 1.002507 0.911855
9600000000 35075543 0.987852 0.998717 1.002669 0.912002
9700000000 17886783 0.988021 0.998890 1.002897 0.912210
9800000000 21437787 0.988085 0.998959 1.003019 0.912321
9900000000 40070955 0.987991 0.998865 1.002978 0.912284
10000000000 18200488 0.988493 0.998686 0.989837 0.912168

yangchuanju · 发表于 2023-3-16 12:24

本帖最后由 yangchuanju 于 2023-3-16 13:10 编辑

（接上楼）
重生、愚公、那宝吉、哈李精度比较表：
10^8-10^10 重生/真值愚公/真值那宝吉/真值哈李/真值
最小 0.987699 0.998558 0.989837 0.890201
最大 0.993055 1.001022 1.006389 0.912321
平均 0.988907 0.999304 0.999544 0.908069
10^7-10^9
最小 0.989027 0.993413 0.990842 0.873075
最大 0.994224 1.001241 1.009126 0.902329
平均 0.990569 0.999642 1.002456 0.897114
精度变化
最小 -0.001327 0.005145 -0.001005 0.017126
最大 -0.001168 -0.000219 -0.002737 0.009991
平均 -0.001662 -0.000338 -0.002912 0.010954
—— 精度略降精度略降精度略升精度升高

yangchuanju · 发表于 2023-3-16 14:15

本帖最后由 yangchuanju 于 2023-3-16 14:28 编辑

愚工688在132楼点评：
杨先生统计的我的修正系数t2=1的时候偶数的大小大约是多少？发表于 2023-3-16 09:45

回复如下：
107楼数据表已经给出，在10^18--10^19时，愚公老师的t2由1.004946降为0.995271。

试差得到：
指数愚公t2
18 1.004946
18.1 1.003966
18.2 1.002990
18.3 1.002016
18.4 1.001044
18.5 1.000076
18.501 1.000066
18.502 1.000056
18.503 1.000047
18.504 1.000037
18.505 1.000027
18.506 1.000018
18.507 1.000008
18.5071 1.000007
18.5072 1.000006
18.5073 1.000005
18.5074 1.000004
18.5075 1.000003
18.5076 1.000002
18.5077 1.000001
18.5078 1.000000
18.5079 0.999999
19 0.995271

即约在3.22*10^18时t2为1。

愚工688 · 发表于 2023-3-16 16:35

本帖最后由愚工688 于 2023-3-16 08:52 编辑

找到了t2＜1的偶数级别的计算程序。

  S( 100000000000000 ) =       ;Xi(M)≈ 88654406718.42          δxi(M)≈  ( t2=  1.046635 )
  S( 1000000000000000 ) =       ;Xi(M)≈ 764214624809.5601       δxi(M)≈  ( t2=  1.035707 )
  S( 1D+16 ) =                ;Xi(M)≈ 6648183549408.48          δxi(M)≈  ( t2=  1.025137 )
  S( 1D+17 ) =                ;Xi(M)≈ 58301987832639.82       δxi(M)≈  ( t2=  1.014893 )
  S( 1D+18 ) =                ;Xi(M)≈ 514942327769236.2       δxi(M)≈  ( t2=  1.004946 )
  S( 1D+19 ) =                ;Xi(M)≈ 4577150636381865          δxi(M)≈  ( t2=  .9952712 )
  S( 1D+20 ) =                ;Xi(M)≈ 4.091767878392376D+16    δxi(M)≈  ( t2=  .9858481 )
  time start =16:37:24, time end =16:37:24

感觉t2的下降速度快了一点，理想的t2应该控制到10^20~25时≤1 。当然现在也不再修正t2了，因为没有大偶数的数据检验。

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