珠联璧合是解决平方加1型素数分布的法宝。

柳林 · 发表于 2017-12-14 14:06

珠联璧合是解决平方加1型素数分布的法宝。

十八世纪伟大的数学家欧拉发现并证明了素数连乘积公式。

这个公式不但可以计算素数个数，也可以计算平方加1型素数的个数。只不过要把公式的N略改一下。也就是说，把区间变大一些。

区间变大的根据也是“算术统宗”。

当然，公式的密度也要改，但是公式的基本形式没有变。也就是说，把P变少一些。

下面，是计算结果，误差率比原公式略微大一些。这也真实的显示了两者的差异。

区间          密度%%          计算值实际值误差误差率
136000 3.675306707 49.98 53 -3.02 -5.6902
164560 3.282149920 54.01 57 -2.99 -5.2438
195840 2.963595682 58.04 62 -3.96 -6.3886
229840 2.698390561 62.02 67 -4.98 -7.4331
266560 2.474009990 65.95 69 -3.05 -4.4243
306000 2.281938305 69.83 71 -1.17 -1.6517
348160 2.116264502 73.68 75 -1.32 -1.7602
393040 1.971599672 77.49 76 1.49          1.9628
440640 1.844389745 81.27 81 0.27 0.3348
490960 1.731924953 85.03 87 -1.97 -2.2637
544000 1.631752303 88.77 90 -1.23 -1.3696
599760 1.541884119 92.48 94 -1.52 -1.6212
658240 1.460802226 96.16 96 0.16          0.1623
719440 1.387271619 99.81 98 1.81 1.8427
783360 1.320491205 103.44 100 3.44          3.4420
850000 1.259405907 107.05 104 3.05    2.9322
919360 1.203403059 110.64 108 2.64          2.4408
991440 1.151921214 114.21 111 3.21    2.8884

柳林 · 发表于 2017-12-14 14:07

1066240 1.104504244 117.77 113 4.77 4.2183
1143760 1.060660614 121.31 117 4.31 3.6873
1224000 1.020106058 124.86 122 2.86 2.3451
1306960 0.982333160 128.39 124 4.39 3.5379
1392640 0.947108606 131.90 130 1.90 1.4601
1481040 0.914158711 135.39 132 3.39 2.5686
1572160 0.883290271 138.87 134 4.87 3.6324
1666000 0.854398128 142.34 137 5.34 3.8998
1762560 0.827216005 145.80 143 2.80 1.9593
1861840 0.801635965 149.25 146 3.25 2.2273
1963840 0.777510259 152.69 150 2.69 1.7937
2068560 0.754715117 156.12 156 0.12 0.0752
2176000 0.733134010 159.53 159 0.53 0.3333
2286160 0.712712722 162.94 161 1.94 1.2034
2399040 0.693321245 166.33 163 3.33 2.0433
2514640 0.674896921 169.71 170 -0.29 -0.1692
2632960 0.657357926 173.08 173 0.08 0.0461
2754000 0.640659617 176.44 176 0.44 0.2487
2877760 0.624771968 179.79 182 -2.21 -1.2119
3004240 0.609613953 183.14 184 -0.86 -0.4659
3133440 0.595133111 186.48 187 -0.52 -0.2773
3265360 0.581282855 189.81 191 -1.19 -0.6232
3400000 0.568019017 193.13 193 0.13 0.0655
3537360 0.555309865 196.43 197 -0.57 -0.2878
3677440 0.543127799 199.73 200 -0.27 -0.1340
3820240 0.531446129 203.03 202 1.03 0.5075
3965760 0.520236380 206.31 208 -1.69 -0.8109
4114000 0.509466549 209.59 210 -0.41 -0.1931
4264960 0.499116789 212.87 215 -2.13 -0.9901
4418640 0.489150681 216.14 221 -4.86 -2.2000
4575040 0.479561774 219.40 226 -6.60 -2.9197
4734160 0.470325932 222.66 228 -5.34 -2.3422
4896000 0.461418446 225.91 229 -3.09 -1.3491
5060560 0.452826512 229.16 230 -0.84 -0.3671
5227840 0.444529742 232.39 233 -0.61 -0.2605
5397840 0.436515872 235.62 238 -2.38 -0.9982
5570560 0.428769481 238.85 243 -4.15 -1.7084
5746000 0.421280234 242.07 244 -1.93 -0.7920
5924160 0.414034826 245.28 248 -2.72 -1.0964
6105040 0.407020054 248.49 253 -4.51 -1.7836
6288640 0.400234189 251.69 254 -2.31 -0.9083
6474960 0.393658572 254.89 257 -2.11 -0.8201
6664000 0.387286131 258.09 260 -1.91 -0.7356
6855760 0.381105638 261.28 263 -1.72 -0.6552
7050240 0.375106748 264.46 266 -1.54 -0.5792
7247440 0.369283308 267.64 270 -2.36 -0.8756
7447360 0.363628665 270.81 272 -1.19 -0.4385
7650000 0.358135704 273.97 277 -3.03 -1.0925
7855360 0.352797990 277.14 282 -4.86 -1.7250
8063440 0.347611502 280.29 286 -5.71 -1.9949
8274240 0.342568083 283.45 289 -5.55 -1.9207
8487760 0.337663776 286.60 293 -6.40 -2.1840
8704000 0.332890222 289.75 298 -8.25 -2.7692
8922960 0.328244219 292.89 302 -9.11 -3.0162
9144640 0.323718478 296.03 303 -6.97 -2.3007
9369040 0.319309376 299.16 306 -6.84 -2.2346
9596160 0.315014598 302.29 308 -5.71 -1.8529
9826000 0.310830522 305.42 311 -5.58 -1.7935
10058560 0.306749492 308.55 315 -6.45 -2.0489
10293840 0.302768756 311.67 319 -7.33 -2.2993
10531840 0.298886222 314.78 322 -7.22 -2.2416
10772560 0.295095725 317.89 327 -9.11 -2.7848
11016000 0.291396847 321.00 331 -10.00 -3.0203
11262160 0.287785595 324.11 335 -10.89 -3.2511
11511040 0.284257338 327.21 339 -11.79 -3.4779
11762640 0.280808820 330.31 339 -8.69 -2.5648
12016960 0.277439866 333.40 341 -7.60 -2.2292
12274000 0.274145313 336.49 344 -7.51 -2.1843
12533760 0.270925950 339.57 350 -10.43 -2.9794
12796240 0.267779275 342.66 350 -7.34 -2.0981
13061440 0.264700366 345.74 350 -4.26 -1.2181
13329360 0.261688795 348.81 353 -4.19 -1.1857
13600000 0.258740875 351.89 356 -4.11 -1.1552
13873360 0.255855010 354.96 357 -2.04 -0.5723
14149440 0.253028552 358.02 362 -3.98 -1.0991
14428240 0.250260544 361.08 368 -6.92 -1.8799
14709760 0.247549324 364.14 371 -6.86 -1.8493
14994000 0.244893288 367.19 373 -5.81 -1.5568
15280960 0.242291538 370.24 377 -6.76 -1.7918
15570640 0.239741000 373.29 379 -5.71 -1.5060
15863040 0.237240540 376.34 381 -4.66 -1.2242

柳林 · 发表于 2017-12-14 14:10

四亿以后误差率小于1%

400994640 0.039205941 1572.14 1559 13.14 0.8427
402472960 0.039126409 1574.73 1561 13.73 0.8797
403954000 0.039047183 1577.33 1565 12.33 0.7876
405437760 0.038968263 1579.92 1568 11.92 0.7602
406924240 0.038889647 1582.51 1573 9.51 0.6048
408413440 0.038811329 1585.11 1575 10.11 0.6417
409905360 0.038733315 1587.70 1578 9.70 0.6147
411400000 0.038655599 1590.29 1582 8.29 0.5241
412897360 0.038578177 1592.88 1584 8.88 0.5608
414397440 0.038501051 1595.47 1585 10.47 0.6608
415900240 0.038424219 1598.06 1589 9.06 0.5704
417405760 0.038347676 1600.65 1592 8.65 0.5436
418914000 0.038271422 1603.24 1593 10.24 0.6430
420424960 0.038195454 1605.83 1596 9.83 0.6161
421938640 0.038119776 1608.42 1598 10.42 0.6521
423455040 0.038044383 1611.01 1600 11.01 0.6880
424974160 0.037969276 1613.60 1602 11.60 0.7239
426496000 0.037894455 1616.18 1607 9.18 0.5715
428020560 0.037819923 1618.77 1611 7.77 0.4823
429547840 0.037745681 1621.36 1612 9.36 0.5805
431077840 0.037671720 1623.94 1616 7.94 0.4916
432610560 0.037598030 1626.53 1616 10.53 0.6516
434146000 0.037524614 1629.12 1619 10.12 0.6248
435684160 0.037451471 1631.70 1620 11.70 0.7223
437225040 0.037378596 1634.29 1621 13.29 0.8196
438768640 0.037305996 1636.87 1622 14.87 0.9168
440314960 0.037233662 1639.45 1625 14.45 0.8895
441864000 0.037161590 1642.04 1629 13.04 0.8003
443415760 0.037089788 1644.62 1632 12.62 0.7733
444970240 0.037018252 1647.20 1634 13.20 0.8080
446527440 0.036946975 1649.78 1634 15.78 0.9660
448087360 0.036875964 1652.37 1637 15.37 0.9386
449650000 0.036805214 1654.95 1640 14.95 0.9114
451215360 0.036734723 1657.53 1643 14.53 0.8842
452783440 0.036664489 1660.11 1646 14.11 0.8571
454354240 0.036594513 1662.69 1649 13.69 0.8300
455927760 0.036524786 1665.27 1652 13.27 0.8031
457504000 0.036455319 1667.85 1656 11.85 0.7153
459082960 0.036386111 1670.42 1658 12.42 0.7494
460664640 0.036317156 1673.00 1662 11.00 0.6620
462249040 0.036248453 1675.58 1665 10.58 0.6355
463836160 0.036179997 1678.16 1666 12.16 0.7298
465426000 0.036111782 1680.74 1670 10.74 0.6429
467018560 0.036043813 1683.31 1673 10.31 0.6164
468613840 0.035976090 1685.89 1674 11.89 0.7102
470211840 0.035908606 1688.47 1675 13.47 0.8039
471812560 0.035841366 1691.04 1676 15.04 0.8974
473416000 0.035774369 1693.62 1678 15.62 0.9306
475022160 0.035707608 1696.19 1680 16.19 0.9637
476631040 0.035641089 1698.76 1684 14.76 0.8768
478242640 0.035574808 1701.34 1686 15.34 0.9098
479856960 0.035508762 1703.91 1691 12.91 0.7636
481474000 0.035442952 1706.49 1697 9.49 0.5590
483093760 0.035377373 1709.06 1700 9.06 0.5329
484716240 0.035312031 1711.63 1704 7.63 0.4479
486341440 0.035246923 1714.20 1706 8.20 0.4809
487969360 0.035182045 1716.78 1709 7.78 0.4550
489600000 0.035117403 1719.35 1710 9.35 0.5467
491233360 0.035052988 1721.92 1713 8.92 0.5207
492869440 0.034988797 1724.49 1716 8.49 0.4948

		自动登录	找回密码
密码			注册