探索高精度计算素数对个数的弥合计算公式

yangchuanju · 发表于 2023-3-15 20:32

本帖最后由 yangchuanju 于 2023-3-15 20:44 编辑

重生、愚公、那宝吉计算式对比2（偶数10^7--10^9）:
求1,2,3……100*10^7共100个偶数的单计素数对，当采用哈李计算式时为0.660161816*N/ln(N)^2*波动系数，因偶数为有限的，计算值小于真实值；
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       位数       波动系数       N/ln(N)^2       重生F       （1+F/ln(N)       重生计算值
10000000       8       1.333333       38492.18306       3.235256       1.200722       38515.34256
20000000       8       1.333333       70766.92957       3.235256       1.192446       70321.45165
30000000       8       2.666667       101209.4419       3.235256       1.187914       200380.1487
40000000       8       1.333333       130546.7393       3.235256       1.184825       128895.9138
50000000       8       1.333333       159101.1694       3.235256       1.182499       156780.8059
60000000       8       2.666667       187054.0454       3.235256       1.180641       368072.8315
70000000       8       1.600000       214521.049       3.235256       1.179100       252941.6854
80000000       8       1.333333       241582.1019       3.235256       1.177785       237109.8936
90000000       8       2.666667       268295.5545       3.235256       1.176642       526146.4025
100000000       9       1.333333       294705.7766       3.282875       1.178217       289356.0899
110000000       9       1.481481       320847.5791       3.282875       1.177299       349753.4131
120000000       9       2.666667       346748.9595       3.282875       1.176470       679899.6937
130000000       9       1.454545       372432.8944       3.282875       1.175714       398067.8414
140000000       9       1.600000       397918.5586       3.282875       1.175020       467562.2338
150000000       9       2.666667       423222.1812       3.282875       1.174379       828371.7315
160000000       9       1.333333       448357.6652       3.282875       1.173783       438562.0852
170000000       9       1.422222       473337.0458       3.282875       1.173227       493628.2033
180000000       9       2.666667       498170.8368       3.282875       1.172706       973679.8422
190000000       9       1.411765       522868.2964       3.282875       1.172216       540807.0332
200000000       9       1.333333       547437.6364       3.282875       1.171754       534551.8443
210000000       9       3.200000       571886.1862       3.282875       1.171317       1339719.619
220000000       9       1.481481       596220.5255       3.282875       1.170902       646403.3898
230000000       9       1.396825       620446.5918       3.282875       1.170507       634016.5989
240000000       9       2.666667       644569.7679       3.282875       1.170131       1257051.904
250000000       9       1.333333       668594.9554       3.282875       1.169772       651753.0236
260000000       9       1.454545       692526.6345       3.282875       1.169428       736236.5912
270000000       9       2.666667       716368.9155       3.282875       1.169099       1395843.569
280000000       9       1.600000       740125.5821       3.282875       1.168783       865046.0249
290000000       9       1.382716       763800.1277       3.282875       1.168479       771282.6938
300000000       9       2.666667       787395.7871       3.282875       1.168186       1533041.47
310000000       9       1.379310       810915.5639       3.282875       1.167904       816441.0655
320000000       9       1.333333       834362.2534       3.282875       1.167632       811856.6727
330000000       9       2.962963       857738.4636       3.282875       1.167369       1854254.159
340000000       9       1.422222       881046.6331       3.282875       1.167115       914028.7909
350000000       9       1.600000       904289.0462       3.282875       1.166868       1055186.284
360000000       9       2.666667       927467.8474       3.282875       1.166630       1803352.665
370000000       9       1.371429       950585.0533       3.282875       1.166398       950366.4387
380000000       9       1.411765       973642.5637       3.282875       1.166174       1001855.635
390000000       9       2.909091       996642.1709       3.282875       1.165956       2112800.823
400000000       9       1.333333       1019585.569       3.282875       1.165743       990479.2923
410000000       9       1.367521       1042474.361       3.282875       1.165537       1038497.841
420000000       9       3.200000       1065310.065       3.282875       1.165336       2482888.625
430000000       9       1.365854       1088094.124       3.282875       1.165140       1082253.316
440000000       9       1.481481       1110827.907       3.282875       1.164950       1198202.415
450000000       9       2.666667       1133512.717       3.282875       1.164764       2200457.31
460000000       9       1.396825       1156149.795       3.282875       1.164582       1175455.925
470000000       9       1.362963       1178740.324       3.282875       1.164405       1169193.002
480000000       9       2.666667       1201285.432       3.282875       1.164232       2330957.564
490000000       9       1.600000       1223786.199       3.282875       1.164062       1424563.538
500000000       9       1.333333       1246243.655       3.282875       1.163897       1208749.33
510000000       9       2.844444       1268658.788       3.282875       1.163735       2624680.42
520000000       9       1.454545       1291032.544       3.282875       1.163577       1365650.302
530000000       9       1.359477       1313365.828       3.282875       1.163422       1298299.047
540000000       9       2.666667       1335659.511       3.282875       1.163270       2589553.576
550000000       9       1.481481       1357914.429       3.282875       1.163121       1462424.516
560000000       9       1.600000       1380131.384       3.282875       1.162975       1605058.1
570000000       9       2.823529       1402311.149       3.282875       1.162832       2877621.124
580000000       9       1.382716       1424454.466       3.282875       1.162691       1431284.824
590000000       9       1.356725       1446562.051       3.282875       1.162554       1426008.101
600000000       9       2.666667       1468634.594       3.282875       1.162419       2845280.185
610000000       9       1.355932       1490672.759       3.282875       1.162286       1468294.789
620000000       9       1.379310       1512677.189       3.282875       1.162156       1515488.034
630000000       9       3.200000       1534648.503       3.282875       1.162027       3566607.368
640000000       9       1.333333       1556587.299       3.282875       1.161902       1507167.738
650000000       9       1.454545       1578494.156       3.282875       1.161778       1667145.128
660000000       9       2.962963       1600369.633       3.282875       1.161656       3442739.704
670000000       9       1.353846       1622214.271       3.282875       1.161537       1594374.993
680000000       9       1.422222       1644028.593       3.282875       1.161419       1697249.808
690000000       9       2.793651       1665813.108       3.282875       1.161303       3377723.037
700000000       9       1.600000       1687568.307       3.282875       1.161189       1959586.172
710000000       9       1.352657       1709294.666       3.282875       1.161077       1677821.233
720000000       9       2.666667       1730992.647       3.282875       1.160967       3349374.413
730000000       9       1.352113       1752662.699       3.282875       1.160858       1719373.674
740000000       9       1.371429       1774305.257       3.282875       1.160751       1765307.971
750000000       9       2.666667       1795920.744       3.282875       1.160645       3474044.214
760000000       9       1.411765       1817509.57       3.282875       1.160541       1861142.094
770000000       9       1.777778       1839072.134       3.282875       1.160438       2371255.55
780000000       9       2.909091       1860608.824       3.282875       1.160337       3925334.314
790000000       9       1.350649       1882120.018       3.282875       1.160238       1843388.581
800000000       9       1.333333       1903606.082       3.282875       1.160139       1840373.54
810000000       9       2.666667       1925067.373       3.282875       1.160042       3721932.734
820000000       9       1.367521       1946504.24       3.282875       1.159947       1929778.7
830000000       9       1.349794       1967917.021       3.282875       1.159852       1925559.924
840000000       9       3.200000       1989306.045       3.282875       1.159759       4614231.52
850000000       9       1.422222       2010671.635       3.282875       1.159667       2072630.938
860000000       9       1.365854       2032014.104       3.282875       1.159576       2011454.702
870000000       9       2.765432       2053333.757       3.282875       1.159487       4114985.855
880000000       9       1.481481       2074630.893       3.282875       1.159398       2227151.281
890000000       9       1.348659       2095905.802       3.282875       1.159311       2048112.575
900000000       9       2.666667       2117158.768       3.282875       1.159224       4090437.155
910000000       9       1.745455       2138390.068       3.282875       1.159139       2704027.371
920000000       9       1.396825       2159599.973       3.282875       1.159055       2185241.674
930000000       9       2.758621       2180788.748       3.282875       1.158972       4357710.988
940000000       9       1.362963       2201956.649       3.282875       1.158889       2173776.144
950000000       9       1.411765       2223103.93       3.282875       1.158808       2273074.155
960000000       9       2.666667       2244230.837       3.282875       1.158728       4334087.161
970000000       9       1.347368       2265337.611       3.282875       1.158648       2210298.298
980000000       9       1.600000       2286424.488       3.282875       1.158570       2648981.796
990000000       9       2.962963       2307491.699       3.282875       1.158492       4950389.415
1000000000       10       1.333333       2328539.469       3.312287       1.159834       2250599.817

yangchuanju · 发表于 2023-3-15 20:33

（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
10000000 1.137832 38551.36872 0.749398 38461.26841 33881.42596
20000000 1.133148 70583.95796 0.749404 70710.7221 62290.16631
30000000 1.130452 201415.2709 0.749409 202259.5045 178172.2906
40000000 1.128559 129681.9264 0.749408 130443.6841 114909.2967
50000000 1.127101 157843.0398 0.749409 158975.7369 140043.3559
60000000 1.125917 370759.7522 0.749411 373814.1633 329295.8354
70000000 1.124920 254895.4269 0.749410 257222.7724 226589.7684
80000000 1.124060 239025.1168 0.749410 241392.0314 212644.3722
90000000 1.123305 530554.6447 0.749411 536169.8482 472315.948
100000000 1.122630 291215.5777 0.736658 289462.9996 259404.6675
110000000 1.122022 352084.4879 0.736658 350155.4243 313794.5488
120000000 1.121469 684575.5492 0.736659 681161.6791 610427.7941
130000000 1.120960 400881.4153 0.736658 399062.856 357623.2377
140000000 1.120491 470947.8015 0.736658 469008.0247 420305.0212
150000000 1.120054 834500.4389 0.736659 831387.6078 745053.6632
160000000 1.119647 441870.2013 0.736658 440381.8255 394651.4806
170000000 1.119264 497417.5179 0.736658 495911.397 444414.64
180000000 1.118905 981274.5614 0.736659 978618.6402 876995.6381
190000000 1.118565 545087.5068 0.736658 543776.9819 487309.6717
200000000 1.118243 538840.1901 0.736658 537699.4247 481863.2323
210000000 1.117937 1350602.015 0.736659 1348112.469 1208119.754
220000000 1.117646 651715.1434 0.736659 650682.9647 583114.1109
230000000 1.117368 639283.0253 0.736659 638429.2895 572132.9062
240000000 1.117102 1267599.285 0.736659 1266208.399 1134720.929
250000000 1.116848 657273.5107 0.736659 656701.6738 588507.8132
260000000 1.116603 742528.3062 0.736659 742044.7993 664988.5682
270000000 1.116368 1407872.41 0.736659 1407252.458 1261118.411
280000000 1.116142 872559.8373 0.736659 872352.098 781764.2374
290000000 1.115924 778032.4105 0.736659 777999.1052 697209.2357
300000000 1.115713 1546553.147 0.736659 1546779.439 1386156.354
310000000 1.115510 823685.5943 0.736659 823955.9976 738393.7811
320000000 1.115313 819106.9319 0.736659 819520.4077 734418.8005
330000000 1.115123 1870915.204 0.736659 1872180.493 1677766.465
340000000 1.114938 922289.7687 0.736659 923066.0706 827211.8688
350000000 1.114759 1064776.49 0.736659 1065844.212 955163.3582
360000000 1.114584 1819830.618 0.736659 1821940.533 1632743.622
370000000 1.114415 959094.9709 0.736659 960352.3855 860626.2241
380000000 1.114251 1011102.468 0.736659 1012577.642 907428.2018
390000000 1.114090 2132393.794 0.736659 2135812.782 1914022.125
400000000 1.113934 999706.334 0.736659 1001449.088 897455.281
410000000 1.113782 1048214.666 0.736659 1050185.402 941130.6216
420000000 1.113634 2506218.292 0.736659 2511265.669 2250486.487
430000000 1.113489 1092463.833 0.736659 1094805.88 981117.5319
440000000 1.113348 1209551.35 0.736659 1212298.377 1086409.139
450000000 1.113210 2221378.492 0.736659 2226700.281 1995471.504
460000000 1.113075 1186672.837 0.736659 1189659.669 1066121.325
470000000 1.112943 1180389.834 0.736659 1183501.202 1060602.377
480000000 1.112814 2353356.962 0.736659 2359834.714 2114780.727
490000000 1.112687 1438298.594 0.736659 1442421.179 1292635.071
500000000 1.112563 1220441.292 0.736659 1224075.523 1096963.3
510000000 1.112442 2650148.034 0.736659 2658330.328 2382279.366
520000000 1.112323 1378941.746 0.736659 1383346.687 1239695.111
530000000 1.112207 1310972.364 0.736659 1315297.975 1178712.848
540000000 1.112092 2614904.115 0.736659 2623802.55 2351337.09
550000000 1.111980 1476780.997 0.736659 1481955.602 1328064.082
560000000 1.111870 1620857.645 0.736659 1626698.238 1457776.066
570000000 1.111762 2906022.23 0.736659 2916777.972 2613888.775
580000000 1.111656 1445447.502 0.736659 1450935.587 1300265.309
590000000 1.111551 1440153.988 0.736659 1445757.65 1295625.07
600000000 1.111449 2873574.195 0.736659 2885022.161 2585430.614
610000000 1.111348 1482930.623 0.736659 1488973.107 1334352.862
620000000 1.111249 1530629.437 0.736659 1537003.376 1377395.476
630000000 1.111152 3602322.637 0.736659 3617642.01 3241972.297
640000000 1.111056 1522293.658 0.736659 1528898.971 1370132.664
650000000 1.110961 1683912.796 0.736659 1691363.153 1515725.918
660000000 1.110868 3477439.015 0.736659 3493117.637 3130379.032
670000000 1.110777 1610477.878 0.736659 1617871.832 1449866.229
680000000 1.110687 1714426.339 0.736659 1722437.291 1543573.194
690000000 1.110598 3411973.851 0.736659 3428191.537 3072195.117
700000000 1.110511 1979495.184 0.736659 1989060.352 1782509.053
710000000 1.110424 1694899.804 0.736659 1703221.825 1526353.139
720000000 1.110339 3383530.861 0.736659 3400404.948 3047293.998
730000000 1.110256 1736939.382 0.736659 1745733.007 1564449.789
740000000 1.110173 1783374.972 0.736659 1792537.014 1606393.482
750000000 1.110092 3509661.06 0.736659 3527951.342 3161595.465
760000000 1.110011 1880255.543 0.736659 1890190.759 1693906.473
770000000 1.109932 2395648.405 0.736659 2408479.103 2158373.688
780000000 1.109854 3965779.935 0.736659 3987301.421 3573244.8
790000000 1.109777 1862412.878 0.736659 1872649.657 1678186.909
800000000 1.109701 1859396.639 0.736659 1869745.202 1675584.064
810000000 1.109625 3760464.109 0.736659 3781650.244 3388949.261
820000000 1.109551 1949787.07 0.736659 1960902.906 1757275.588
830000000 1.109478 1945554.276 0.736659 1956775.342 1753576.647
840000000 1.109405 4662214.145 0.736659 4689410.925 4202444.453
850000000 1.109334 2094214.82 0.736659 2106566.813 1887813.174
860000000 1.109263 2032431.041 0.736659 2044548.938 1832235.483
870000000 1.109193 4157958.186 0.736659 4183013.329 3748633.203
880000000 1.109124 2250440.823 0.736659 2264142.228 2029025.33
890000000 1.109056 2069558.54 0.736659 2082286.774 1866054.472
900000000 1.108988 4133324.794 0.736659 4158999.433 3727113.006
910000000 1.108922 2732415.356 0.736659 2749553.245 2464029.331
920000000 1.108856 2208212.397 0.736659 2222194.511 1991433.631
930000000 1.108790 4403575.444 0.736659 4431719.789 3971512.993
940000000 1.108726 2196683.05 0.736659 2210850.889 1981267.976
950000000 1.108662 2297056.431 0.736659 2312004.775 2071917.639
960000000 1.108599 4379868.788 0.736659 4408623.014 3950814.679
970000000 1.108536 2233673.377 0.736659 2248463.987 2014975.179
980000000 1.108475 2677028.501 0.736659 2694905.279 2415056.228
990000000 1.108413 5002862.324 0.736659 5036549.249 4513534.549
1000000000 1.108353 2271699.063 0.725791 2253378.632 2049617.126

yangchuanju · 发表于 2023-3-15 20:35

本帖最后由 yangchuanju 于 2023-3-15 20:47 编辑

（接上楼）
重生、愚公、那宝吉计算式精度对比：
三人精度都非常高，
重生的精度都小于1，最小0.989027，最大0.994224；
愚公的精度有的小于1，有的大于1，最小0.993413，最大1.001241；
那宝吉的精度有的小于1，有的大于1，最小0.990842，最大1.009126；
哈李计算式由于偶数较小（10^7-10^9)，精度较低，仅为0.873——0.902。

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
10000000 38807 0.992484 0.993413 0.991091 0.873075
20000000 70730 0.994224 0.997935 0.999727 0.880675
30000000 202166 0.991166 0.996287 1.000463 0.881317
40000000 130164 0.990258 0.996296 1.002149 0.882804
50000000 158457 0.989422 0.996125 1.003274 0.883794
60000000 371226 0.991506 0.998744 1.006972 0.887049
70000000 255175 0.991248 0.998904 1.008025 0.887978
80000000 239209 0.991225 0.999231 1.009126 0.888948
90000000 531538 0.989857 0.998150 1.008714 0.888584
100000000 291400 0.992986 0.999367 0.993353 0.890201
110000000 352539 0.992099 0.998711 0.993239 0.890099
120000000 684832 0.992798 0.999626 0.994641 0.891354
130000000 401223 0.992136 0.999149 0.994616 0.891333
140000000 471567 0.991508 0.998687 0.994573 0.891294
150000000 835256 0.991758 0.999095 0.995369 0.892006
160000000 442542 0.991007 0.998482 0.995119 0.891783
170000000 496872 0.993472 1.001098 0.998067 0.894425
180000000 981368 0.992166 0.999905 0.997198 0.893646
190000000 545453 0.991482 0.999330 0.996927 0.893404
200000000 538290 0.993055 1.001022 0.998903 0.895174
210000000 1350970 0.991672 0.999728 0.997885 0.894261
220000000 652195 0.991120 0.999264 0.997682 0.894079
230000000 639086 0.992068 1.000308 0.998972 0.895236
240000000 1268606 0.990892 0.999206 0.998110 0.894463
250000000 657736 0.990904 0.999297 0.998427 0.894748
260000000 742738 0.991247 0.999718 0.999067 0.895321
270000000 1407202 0.991928 1.000476 1.000036 0.896189
280000000 873316 0.990530 0.999134 0.998896 0.895168
290000000 778225 0.991079 0.999753 0.999710 0.895897
300000000 1547388 0.990729 0.999460 0.999607 0.895804
310000000 823689 0.991201 0.999996 1.000324 0.896447
320000000 818922 0.991372 1.000226 1.000731 0.896812
330000000 1871659 0.990701 0.999603 1.000279 0.896406
340000000 922302 0.991030 0.999987 1.000828 0.896899
350000000 1065716 0.990120 0.999118 1.000120 0.896264
360000000 1820308 0.990685 0.999738 1.000897 0.896960
370000000 959976 0.989990 0.999082 1.000392 0.896508
380000000 1011694 0.990275 0.999415 1.000873 0.896939
390000000 2132039 0.990977 1.000166 1.001770 0.897743
400000000 999700 0.990777 1.000006 1.001750 0.897725
410000000 1048242 0.990704 0.999974 1.001854 0.897818
420000000 2506411 0.990615 0.999923 1.001937 0.897892
430000000 1092224 0.990871 1.000220 1.002364 0.898275
440000000 1209010 0.991061 1.000448 1.002720 0.898594
450000000 2221139 0.990689 1.000108 1.002504 0.898400
460000000 1186837 0.990411 0.999862 1.002378 0.898288
470000000 1180327 0.990567 1.000053 1.002689 0.898567
480000000 2354108 0.990166 0.999681 1.002433 0.898336
490000000 1438132 0.990565 1.000116 1.002982 0.898829
500000000 1219610 0.991095 1.000682 1.003661 0.899438
510000000 2650162 0.990385 0.999995 1.003082 0.898918
520000000 1379055 0.990280 0.999918 1.003112 0.898945
530000000 1309708 0.991289 1.000965 1.004268 0.899981
540000000 2614820 0.990337 1.000032 1.003435 0.899235
550000000 1476817 0.990254 0.999976 1.003480 0.899275
560000000 1620864 0.990248 0.999996 1.003599 0.899382
570000000 2907122 0.989852 0.999622 1.003321 0.899133
580000000 1444996 0.990511 1.000312 1.004110 0.899840
590000000 1439765 0.990445 1.000270 1.004162 0.899886
600000000 2874881 0.989704 0.999545 1.003528 0.899317
610000000 1482270 0.990572 1.000446 1.004522 0.900209
620000000 1530179 0.990399 1.000294 1.004460 0.900153
630000000 3602533 0.990028 0.999942 1.004194 0.899915
640000000 1522890 0.989676 0.999608 1.003946 0.899692
650000000 1681825 0.991271 1.001241 1.005671 0.901239
660000000 3479340 0.989481 0.999454 1.003960 0.899705
670000000 1610469 0.990007 1.000006 1.004597 0.900276
680000000 1714517 0.989929 0.999947 1.004620 0.900296
690000000 3412326 0.989859 0.999897 1.004649 0.900323
700000000 1979689 0.989845 0.999902 1.004734 0.900399
710000000 1695422 0.989619 0.999692 1.004601 0.900279
720000000 3383300 0.989973 1.000068 1.005056 0.900687
730000000 1738177 0.989182 0.999288 1.004347 0.900052
740000000 1782274 0.990481 1.000618 1.005758 0.901317
750000000 3509767 0.989822 0.999970 1.005181 0.900799
760000000 1879966 0.989987 1.000154 1.005439 0.901030
770000000 2393728 0.990612 1.000802 1.006162 0.901679
780000000 3964603 0.990095 1.000297 1.005725 0.901287
790000000 1861637 0.990198 1.000417 1.005916 0.901458
800000000 1859646 0.989636 0.999866 1.005431 0.901023
810000000 3760240 0.989813 1.000060 1.005694 0.901259
820000000 1950479 0.989387 0.999645 1.005344 0.900946
830000000 1944221 0.990402 1.000686 1.006457 0.901943
840000000 4660941 0.989979 1.000273 1.006108 0.901630
850000000 2093986 0.989802 1.000109 1.006008 0.901540
860000000 2031753 0.990009 1.000334 1.006298 0.901800
870000000 4159646 0.989263 0.999594 1.005618 0.901190
880000000 2250996 0.989407 0.999753 1.005840 0.901390
890000000 2070421 0.989225 0.999583 1.005731 0.901292
900000000 4132595 0.989799 1.000177 1.006389 0.901882
910000000 2734029 0.989027 0.999410 1.005678 0.901245
920000000 2208186 0.989609 1.000012 1.006344 0.901841
930000000 4401400 0.990074 1.000494 1.006889 0.902329
940000000 2197425 0.989238 0.999662 1.006110 0.901632
950000000 2296843 0.989652 1.000093 1.006601 0.902072
960000000 4382119 0.989039 0.999487 1.006048 0.901576
970000000 2234294 0.989260 0.999722 1.006342 0.901840
980000000 2678354 0.989033 0.999505 1.006180 0.901694
990000000 5003457 0.989394 0.999881 1.006614 0.902083
1000000000 2274205 0.989620 0.998898 0.990842 0.901246
———— 最小———— 0.989027 0.993413 0.990842 0.873075
———— 最大———— 0.994224 1.001241 1.009126 0.902329

yangchuanju · 发表于 2023-3-15 20:55

愚工688 发表于 2023-3-15 10:28
使用由素数定理推理出来哈-李计算式经过误差修正，同样能够得到比较高的计算值精度：

偶数素数对计算 ...

愚公老师：
您好！
可否提供11-99亿间每个整亿的素数对数？
请老师抽空算一算，学生先行致谢了！

大傻8888888 · 发表于 2023-3-15 21:14

愚工688给出了不少偶数的实际值，我推测他是根据埃氏筛法编的电脑程序用计算机计算出来的，不知是否如此？
重生888@先生说“使用中国网眼筛子，比埃氏筛法有用！”，不知他的网眼筛子是如何筛的，居然比埃氏筛法还有用。重生888@先生断定202303170的素对真值不小于1140452很好，不知重生888@先生是否可以断定10^3000的素对真值是多少？我用哈李公式得出的素对真值为3.6893×10^2992（双计法并且只保留小数点后5位数）。
我和白新岭先生都是普通的网友，对任何人都没有成见，以前重生888@先生计算素数对只考虑4种偶数类型，后来计算素数对也考虑小于整除根号偶数的素数，这就是进步，值得鼓励。只要重生888@先生用他的的方法在数值充分大时得出的结果和哈李公式的结果吻合，我同样会为他点赞，向他学习！

vfbpgyfk · 发表于 2023-3-15 23:57

@重生888

vfbpgyfk · 发表于 2023-3-16 05:59

本帖最后由 vfbpgyfk 于 2023-3-15 22:15 编辑

先做10个力所能及的间隔亿级连续偶数素数对个数计算，也就20亿级内的十个间隔1亿连续偶数，并给出与新法对比出的计算精度。我的精度计算方法是以【小除大*100】。
为了方便复制，只发十个对应偶数的素数对个数：
D(110000000)=2748595
D(120000000)=5352052
D(130000000)=3137228
D(140000000)=3688114
D(150000000)=6543614
D(160000000)=3467407
D(170000000)=3904453
D(180000000)=7709245
D(190000000)=4284979
D(200000000)=4238418

yangchuanju · 发表于 2023-3-16 07:31

大傻8888888 发表于 2023-3-15 21:14
愚工688给出了不少偶数的实际值，我推测他是根据埃氏筛法编的电脑程序用计算机计算出来的，不知是否如此？
...

估算10^3000的素数对
10^3000超出了常规计算机的数字范围，其素数对数不能用1.32*4/3*N/ln(N)^2直接计算（估算）；
幸好还有常用对数法可用！
lg[1.32*4/3*N/ln(N)^2]=lg(1.32)+lg(4/3)+lg(N)-2*lg(ln(N))
lg(10^n)=n lg(ln(10^n))=lg(n*ln(10))=lg(n)+lg(ln(10))
lg(ln(10))= 0.362215689
lg(1.320323632)= 0.120680397
lg(4/3)= 0.124938737
lg(N)= 3000
2*lg(ln(N))= 7.678673887
lg[1.32*4/3*N/ln(N)^2]= 2992.566945
改成常规指数式为：
指数 2992
系数 3.689310827
即10^3000的双计素数对数等于
3.68931082720343*10^2992

大傻一点也不傻，他的计算结果非常对！
在此给大傻一个大大的赞！

yangchuanju · 发表于 2023-3-16 07:47

本帖最后由 yangchuanju 于 2023-3-18 08:48 编辑

vfbpgyfk 发表于 2023-3-16 05:59
先做10个力所能及的间隔亿级连续偶数素数对个数计算，也就20亿级内的十个间隔1亿连续偶数，并给出与新法对 ...

偶数波动系数 N/ln(N)^2 那宝吉DT 那宝吉计算值真实素数对那宝吉/真实值
1100000000 1.481481 2537994.3 0.725791 2728969.8 2748595 0.992860
1200000000 2.666667 2745721.6 0.725792 5314190.8 5352052 0.992926
1300000000 1.454545 2951884.3 0.725791 3116294.5 3137228 0.993327
1400000000 1.600000 3156618.6 0.725792 3665675.1 3688114 0.993916
1500000000 2.666667 3360039.9 0.725792 6503169.7 6543614 0.993819
1600000000 1.333333 3562247.3 0.725792 3447265.1 3467407 0.994191
1700000000 1.422222 3763326.5 0.725792 3884644.2 3904453 0.994927
1800000000 2.666667 3963352.6 0.725792 7670847.9 7709245 0.995019
1900000000 1.411765 4162391.6 0.725792 4264981.6 4284979 0.995333
2000000000 1.333333 4360502.4 0.725792 4219754.3 4238418 0.995597

谢谢那老师抢先算出11-20亿间的素数对数，学生复核了一下，二人计算的精度相同。

那宝吉的15,20亿素数对各多一个。

cuikun-186 · 发表于 2023-3-16 07:50

本帖最后由 cuikun-186 于 2023-3-16 08:26 编辑

yangchuanju 发表于 2023-3-16 07:31
估算10^3000的素数对
10^3000超出了常规计算机的数字范围，其素数对数不能用1.32*4/3*N/ln(N)^2直接 ...

请注意！！！

你这是哈李公式的主项计算。

余项是多少？显然你没有给出！！！

因此说：10^3000的双计素数对数等于 3.68931082720343*10^2992 （谬！！！）

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