素数连乘积是和氏璧

柳林

素数连乘积是和氏璧
伟大的数学家欧拉发现的素数连乘积是一块从素数宝山上采到得宝玉。
可惜的是，二百多年来被数学家们丢弃了。它的命运还不及卞和手中的何氏璧。卞和虽被昏庸的楚王剁去双脚，但他还是在有生之年得到了世人的认可。
近代数学家把从黄土中得到的所谓素数定理当成宝贝，结果200年素数研究没有任何进展。
和氏璧有暇疵，素数连乘积也有暇疵。不雕琢是不成的，玉不琢不成器吗。
本人对素数连乘积进行了长期的雕琢，取得了较好的效果。它的计算结果比素数定理精确许多倍。

柳林

不说那个素数定理，就是那个比素数定理精确得多的，被叫做"x的积分对数"的公式,,在计算100万以下的素数个数时，误差就有129个，而我的计算误差只有9个。

柳林

有兴趣者可对照下表，看看误差有多大：

区间密度素数个数
100*23.809524 *23.81
400*20.146520 *80.59
900*17.776341 *159.99
1600*16.230572 *259.69
2500*15.353244 *383.83
3600*14.639140 *527.01
4900*14.016198 *686.79
6400*13.487285 *863.19
8100*13.084679 *1059.86
10000*12.726195 *1272.62
12100*12.419539 *1502.76
14400*12.163466 *1751.54
16900*11.927283 *2015.71
19600*11.704343 *2294.05
22500*11.497186 *2586.87
25600*11.316128 *2896.93
28900*11.150929 *3222.62
32400*11.008879 *3566.88
36100*10.873801 *3925.44
40000*10.743576 *4297.43
44100*10.619373 *4683.14
48400*10.509327 *5086.51
52900*10.402634 *5502.99
57600*10.309336 *5938.18
62500*10.218505 *6386.57
67600*10.130793 *6848.42
72900*10.051954 *7327.87
78400*9.975513 *7820.80
84100*9.903488 *8328.83
90000*9.833499 *8850.15
96100*9.766376 *9385.49
102400*9.702751 *9935.62
108900*9.640753 *10498.78
115600*9.579928 *11074.40
122500*9.523074 *11665.77
129600*9.468186 *12270.77
136900*9.414541 *12888.51
144400*9.363236 *13520.51
152100*9.313031 *14165.12
160000*9.264399 *14823.04
168100*9.217727 *15495.00
176400*9.175151 *16184.97
184900*9.133728 *16888.26
193600*9.093756 *17605.51
202500*9.054474 *18335.31
211600*9.015696 *19077.21
220900*8.978671 *19833.88
230400*8.942971 *20604.60
240100*8.908772 *21389.96
250000*8.876199 *22190.50
260100*8.844327 *23004.09
270400*8.812909 *23830.10
280900*8.782361 *24669.65
291600*8.752438 *25522.11
302500*8.722919 *26386.83
313600*8.694178 *27264.94
324900*8.665812 *28155.22
336400*8.637722 *29057.30
348100*8.610855 *29974.39
360000*8.584237 *30903.25
372100*8.557945 *31844.12
384400*8.532513 *32798.98
396900*8.507306 *33765.50
409600*8.482395 *34743.89
422500*8.459060 *35739.53
435600*8.435979 *36747.12
448900*8.413271 *37767.17
462400*8.391043 *38800.18
476100*8.369333 *39846.39
490000*8.348064 *40905.51
504100*8.327115 *41976.99
518400*8.306879 *43062.86
532900*8.286790 *44160.30
547600*8.267360 *45272.06
562500*8.248066 *46395.37
577600*8.228952 *47530.42
592900*8.210185 *48678.19
608400*8.191589 *49837.63
624100*8.173119 *51008.44
640000*8.155097 *52192.62
656100*8.137690 *53391.38
672400*8.120504 *54602.27
688900*8.103462 *55824.75
705600*8.086702 *57059.77
722500*8.070147 *58306.82
739600*8.053728 *59565.37
756900*8.037572 *60836.38
774400*8.021703 *62120.07
792100*8.006172 *63416.89
810000*7.991109 *64727.98
828100*7.976406 *66052.62
846400*7.961810 *67388.76
864900*7.947295 *68736.15
883600*7.932885 *70094.97
902500*7.918681 *71466.09
921600*7.904578 *72848.59
940900*7.890867 *74245.16
960400*7.877297 *75653.56
980100*7.864024 *77075.30
1000000*7.850841 *78508.41

ysr

伯乐爱惜千里马，千里马其不慕伯乐乎，高质量有价值的文章，该受重视

柳林

我不知伯乐在哪里。有伯乐之名的假伯乐都抓钱去了，无伯乐之名的真伯乐说话不管用，实是无可奈何。

柳林

不论如何，还是把一亿以下的计算结果发出来，供大家参考：
区间*密度*素数个数
1000000*7.850841 *78508.41
1020100*7.837896 *79954.38
1040400*7.825015 *81411.46
1060900*7.812219 *82879.83
1081600*7.799588 *84360.34
1102500*7.787373 *85855.78
1123600*7.775233 *87362.52
1144900*7.763244 *88881.38
1166400*7.751328 *90411.49
1188100*7.739466 *91952.60
1210000*7.727802 *93506.40
1232100*7.716496 *95074.94
1254400*7.705255 *96654.72
1276900*7.694426 *98250.12
1299600*7.683642 *99856.61
1322500*7.672918 *101474.34
1345600*7.662312 *103104.08
1368900*7.651766 *104745.02
1392400*7.641446 *106399.50
1416100*7.631169 *108064.98
1440000*7.620946 *109741.62
1464100*7.610938 *111431.75
1488400*7.601073 *113134.37
1512900*7.591284 *114848.54
1537600*7.581595 *116574.61
1562500*7.572016 *118312.76
1587600*7.562534 *120062.78
1612900*7.553122 *121824.30
1638400*7.543756 *123596.90
1664100*7.534483 *125381.33
1690000*7.525278 *127177.20
1716100*7.516195 *128985.42
1742400*7.507156 *130804.68
1768900*7.498149 *132634.75
1795600*7.489291 *134477.71
1822500*7.480464 *136331.47
1849600*7.471781 *138198.07
1876900*7.463158 *140076.02
1904400*7.454615 *141965.68
1932100*7.446110 *143866.28
1960000*7.437729 *145779.49
1988100*7.429386 *147703.62
2016400*7.421071 *149638.48
2044900*7.412930 *151587.00
2073600*7.404903 *153548.06
2102500*7.396970 *155521.30
2131600*7.389072 *157505.45
2160900*7.381198 *159500.31
2190400*7.373457 *161508.21
2220100*7.365748 *163526.98
2250000*7.358127 *165557.86
2280100*7.350668 *167602.59
2310400*7.343270 *169658.90
2340900*7.335901 *171726.10
2371600*7.328554 *173803.98
2402500*7.321236 *175892.70
2433600*7.313977 *177992.94
2464900*7.306760 *180104.33
2496400*7.299642 *182228.26
2528100*7.292565 *184363.34
2560000*7.285563 *186510.42
2592100*7.278581 *188668.11
2624400*7.271692 *190838.29
2656900*7.264887 *193020.77
2689600*7.258106 *195214.03
2722500*7.251364 *197418.39
2755600*7.244781 *199637.18
2788900*7.238216 *201866.60
2822400*7.231674 *204106.77
2856100*7.225209 *206359.18
2890000*7.218766 *208622.34
2924100*7.212398 *210897.72
2958400*7.206051 *213183.83
2992900*7.199750 *215481.31
3027600*7.193470 *217789.50
3062500*7.187207 *220108.20
3097600*7.181045 *222440.06
3132900*7.174926 *224783.25
3168400*7.168838 *227137.45
3204100*7.162806 *229503.46
3240000*7.156794 *231880.13
3276100*7.150813 *234267.78
3312400*7.144896 *236667.53
3348900*7.138998 *239077.91
3385600*7.133139 *241499.57
3422500*7.127309 *243932.16
3459600*7.121531 *246376.49
3496900*7.115772 *248831.42
3534400*7.110026 *251296.77
3572100*7.104345 *253774.31
3610000*7.098758 *256265.15
3648100*7.093205 *258767.22
3686400*7.087734 *261282.23
3724900*7.082317 *263809.24
3763600*7.076938 *266347.63
3802500*7.071591 *268897.24
3841600*7.066268 *271457.74
3880900*7.060961 *274028.82
3920400*7.055685 *276611.09
3960100*7.050426 *279203.92
4000000*7.045178 *281807.12
4040100*7.039946 *284420.85
4080400*7.034745 *287045.72
4120900*7.029559 *289681.08
4161600*7.024452 *292329.59
4202500*7.019374 *294989.21
4243600*7.014319 *297659.65
4284900*7.009304 *300341.65
4326400*7.004302 *303034.13
4368100*6.999357 *305738.93
4410000*6.994423 *308454.06
4452100*6.989503 *311179.65
4494400*6.984610 *313916.30
4536900*6.979771 *316665.23
4579600*6.974952 *319424.92
4622500*6.970147 *322195.05
4665600*6.965368 *324976.22
4708900*6.960609 *327768.11
4752400*6.955894 *330571.93
4796100*6.951190 *333386.01
4840000*6.946498 *336210.49
4884100*6.941902 *339049.44
4928400*6.937330 *341899.40
4972900*6.932807 *344761.54
5017600*6.928309 *347634.84
5062500*6.923892 *350522.03
5107600*6.919514 *353421.10
5152900*6.915144 *356330.47
5198400*6.910805 *359251.27
5244100*6.906489 *362183.21
5290000*6.902196 *365126.15
5336100*6.897952 *368081.62
5382400*6.893716 *371047.39
5428900*6.889547 *374026.62
5475600*6.885388 *377016.31
5522500*6.881244 *380016.70
5569600*6.877127 *383028.47
5616900*6.873018 *386050.53
5664400*6.868942 *389084.37
5712100*6.864910 *392130.53
5760000*6.860887 *395187.11
5808100*6.856890 *398255.05
5856400*6.852923 *401334.60
5904900*6.848966 *404424.57
5953600*6.845015 *407524.79
6002500*6.841122 *410638.35
6051600*6.837243 *413762.59
6100900*6.833372 *416897.21
6150400*6.829519 *420042.75
6200100*6.825679 *423198.94
6250000*6.821869 *426366.82
6300100*6.818072 *429545.35
6350400*6.814291 *432734.76
6400900*6.810519 *435934.53
6451600*6.806753 *439144.51
6502500*6.802996 *442364.81
6553600*6.799255 *445595.97
6604900*6.795522 *448837.44
6656400*6.791822 *452090.83
6708100*6.788128 *455354.39
6760000*6.784455 *458629.19
6812100*6.780815 *461915.88
6864400*6.777182 *465212.87
6916900*6.773584 *468522.01
6969600*6.770012 *471842.76
7022500*6.766446 *475173.68
7075600*6.762888 *478514.87
7128900*6.759350 *481867.27
7182400*6.755823 *485230.21
7236100*6.752310 *488603.93
7290000*6.748805 *491987.92
7344100*6.745311 *495382.41
7398400*6.741832 *498787.68
7452900*6.738381 *502204.77
7507600*6.734940 *505632.35
7562500*6.731506 *509070.17
7617600*6.728092 *512519.14
7672900*6.724683 *515978.19
7728400*6.721292 *519448.37
7784100*6.717934 *522930.73
7840000*6.714581 *526423.17
7896100*6.711235 *529925.81
7952400*6.707902 *533439.18
8008900*6.704595 *536964.30
8065600*6.701303 *540500.27
8122500*6.698028 *544047.34
8179600*6.694782 *547606.41
8236900*6.691543 *551175.67
8294400*6.688320 *554756.02
8352100*6.685102 *558346.42
8410000*6.681901 *561947.90
8468100*6.678732 *565561.72
8526400*6.675584 *569187.00
8584900*6.672445 *572822.72
8643600*6.669322 *576469.50
8702500*6.666207 *580126.71
8761600*6.663105 *583794.59
8820900*6.660025 *587474.14
8880400*6.656954 *591164.12
8940100*6.653898 *594865.13
9000000*6.650848 *598576.30
9060100*6.647806 *602297.87
9120400*6.644782 *606030.72
9180900*6.641778 *609774.96
9241600*6.638791 *613530.46
9302500*6.635811 *617296.36
9363600*6.632838 *621072.40
9424900*6.629879 *624859.43
9486400*6.626927 *628656.85
9548100*6.623987 *632464.88
9610000*6.621051 *636283.02
9672100*6.618120 *640111.15
9734400*6.615193 *643949.36
9796900*6.612283 *647798.80
9859600*6.609388 *651659.20
9922500*6.606503 *655530.31
9985600*6.603629 *659412.00
10048900*6.600760 *663303.77
10112400*6.597913 *667207.35
10176100*6.595071 *671121.01
10240000*6.592239 *675045.23
10304100*6.589411 *678979.51
10368400*6.586591 *682924.09
10432900*6.583790 *686880.21
10497600*6.581002 *690847.25
10562500*6.578221 *694824.59
10627600*6.575470 *698814.68
10692900*6.572723 *702814.71
10758400*6.569980 *706824.78
10824100*6.567250 *710845.75
10890000*6.564524 *714876.63
10956100*6.561832 *718920.84
11022400*6.559155 *722976.30
11088900*6.556496 *727043.25
11155600*6.553840 *731120.13
11222500*6.551188 *735207.06
11289600*6.548545 *739304.50
11356900*6.545908 *743412.21
11424400*6.543275 *747529.94
11492100*6.540651 *751658.17
11560000*6.538031 *755796.40
11628100*6.535418 *759944.89
11696400*6.532815 *764104.21
11764900*6.530242 *768276.42
11833600*6.527674 *772458.88
11902500*6.525118 *776652.18
11971600*6.522566 *780855.47
12040900*6.520031 *785070.43
12110400*6.517501 *789295.39
12180100*6.514978 *793530.82
12250000*6.512471 *797777.66
12320100*6.509979 *802035.90
12390400*6.507491 *806304.13
12460900*6.505006 *810582.24
12531600*6.502538 *814872.08
12602500*6.500083 *819172.97
12673600*6.497632 *823483.84
12744900*6.495190 *827805.50
12816400*6.492754 *832137.38
12888100*6.490326 *836479.69
12960000*6.487916 *840833.94
13032100*6.485510 *845198.17
13104400*6.483111 *849572.83
13176900*6.480716 *853957.45
13249600*6.478323 *858351.90
13322500*6.475940 *862757.12
13395600*6.473561 *867172.28
13468900*6.471197 *871599.00
13542400*6.468836 *876035.67
13616100*6.466485 *880483.08
13690000*6.464137 *884940.31
13764100*6.461798 *889408.28
13838400*6.459472 *893887.56
13912900*6.457150 *898376.77
13987600*6.454832 *902876.13
14062500*6.452536 *907387.94
14137600*6.450251 *911910.71
14212900*6.447969 *916443.40
14288400*6.445689 *920985.89
14364100*6.443421 *925539.44
14440000*6.441157 *930103.13
14516100*6.438904 *934677.76
14592400*6.436659 *939263.09
14668900*6.434418 *943858.32
14745600*6.432193 *948465.38
14822500*6.429977 *953083.37
14899600*6.427765 *957711.27
14976900*6.425559 *962349.51
15054400*6.423359 *966998.21
15132100*6.421166 *971657.25
15210000*6.418977 *976326.41
15288100*6.416800 *981006.80
15366400*6.414626 *985697.08
15444900*6.412460 *990398.02
15523600*6.410296 *995108.73
15602500*6.408142 *999830.43
15681600*6.406002 *1004563.58
15760900*6.403869 *1009307.38
15840400*6.401747 *1014062.40
15920100*6.399629 *1018827.28
16000000*6.397512 *1023601.93
16080100*6.395398 *1028386.43
16160400*6.393290 *1033181.23
16240900*6.391184 *1037985.88
16321600*6.389093 *1042802.28
16402500*6.387010 *1047629.31
16483600*6.384930 *1052466.40
16564900*6.382858 *1057314.12
16646400*6.380790 *1062171.91
16728100*6.378731 *1067040.53
16810000*6.376675 *1071918.99
16892100*6.374623 *1076807.72
16974400*6.372582 *1081707.61
17056900*6.370545 *1086617.55
17139600*6.368511 *1091537.31
17222500*6.366482 *1096467.33
17305600*6.364457 *1101407.39
17388900*6.362442 *1106358.60
17472400*6.360429 *1111319.61
17556100*6.358422 *1116290.86
17640000*6.356417 *1121271.92
17724100*6.354416 *1126263.00
17808400*6.352420 *1131264.31
17892900*6.350426 *1136275.40
17977600*6.348441 *1141297.27
18062500*6.346465 *1146330.27
18147600*6.344504 *1151375.25
18232900*6.342566 *1156433.73
18318400*6.340630 *1161502.02
18404100*6.338698 *1166580.33
18490000*6.336771 *1171668.87
18576100*6.334852 *1176768.51
18662400*6.332943 *1181879.23
18748900*6.331040 *1187000.29
18835600*6.329142 *1192131.89
18922500*6.327254 *1197274.57
19009600*6.325374 *1202428.33
19096900*6.323496 *1207591.78
19184400*6.321626 *1212766.09
19272100*6.319765 *1217951.46
19360000*6.317907 *1223146.83
19448100*6.316055 *1228352.74
19536400*6.314205 *1233568.33
19624900*6.312357 *1238793.71
19713600*6.310516 *1244029.81
19802500*6.308677 *1249275.69
19891600*6.306844 *1254532.09
19980900*6.305017 *1259799.20
20070400*6.303194 *1265076.30
20160100*6.301380 *1270364.43
20250000*6.299571 *1275663.06
20340100*6.297765 *1280971.67
20430400*6.295961 *1286290.04
20520900*6.294162 *1291618.59
20611600*6.292367 *1296957.42
20702500*6.290576 *1302306.42
20793600*6.288789 *1307665.69
20884900*6.287007 *1313035.12
20976400*6.285237 *1318416.40
21068100*6.283473 *1323808.37
21160000*6.281722 *1329212.37
21252100*6.279974 *1334626.33
21344400*6.278228 *1340050.04
21436900*6.276485 *1345483.92
21529600*6.274745 *1350927.54
21622500*6.273011 *1356381.82
21715600*6.271279 *1361845.85
21808900*6.269548 *1367319.50
21902400*6.267819 *1372802.88
21996100*6.266098 *1378297.22
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90440100*5.746360 *5197013.74
90630400*5.745650 *5207305.82
90820900*5.744942 *5217607.73
91011600*5.744233 *5227918.75
91202500*5.743527 *5238239.83
91393600*5.742820 *5248570.32
91584900*5.742115 *5258909.92
91776400*5.741411 *5269260.77
91968100*5.740710 *5279621.66
92160000*5.740010 *5289993.55
92352100*5.739312 *5300374.71
92544400*5.738613 *5310764.97
92736900*5.737915 *5321164.65
92929600*5.737218 *5331573.44
93122500*5.736521 *5341992.04
93315600*5.735825 *5352419.89
93508900*5.735130 *5362856.84
93702400*5.734437 *5373304.78
93896100*5.733744 *5383761.82
94090000*5.733052 *5394228.27
94284100*5.732360 *5404703.81
94478400*5.731669 *5415189.39
94672900*5.730979 *5425683.99
94867600*5.730290 *5436188.47
95062500*5.729602 *5446702.74
95257600*5.728915 *5457226.49
95452900*5.728228 *5467759.89
95648400*5.727542 *5478302.53
95844100*5.726858 *5488855.75
96040000*5.726175 *5499418.45
96236100*5.725493 *5509990.94
96432400*5.724812 *5520573.69
96628900*5.724132 *5531166.08
96825600*5.723454 *5541768.88
97022500*5.722777 *5552381.31
97219600*5.722101 *5563003.53
97416900*5.721425 *5573635.00
97614400*5.720750 *5584275.55
97812100*5.720075 *5594925.74
98010000*5.719402 *5605585.70
98208100*5.718729 *5616254.75
98406400*5.718057 *5626933.97
98604900*5.717386 *5637622.27
98803600*5.716715 *5648319.96
99002500*5.716044 *5659026.73
99201600*5.715375 *5669743.28
99400900*5.714706 *5680469.29
99600400*5.714038 *5691204.68
99800100*5.713370 *5701949.30
100000000*5.712703 *5712703.00

ysr

有用的东西连专家也不重视，希望你能继续，最好搞出质数公式，这是难题

柳林

我的公式早已成功，前面的结果就是用公式计算得到的。只不过没有得到权威的评审与认可。
早在2000年，某省数学会副会长曾帮我核对过计算值与实际值的误差。但因其不是数论专家，无推荐之责权，实是遗憾。

申一言

   可惜呀！
        可惜是和氏假壁！
   不符合自然法则的东西哪能顺理成章的推导出素数（质数）或单位的定理来？！[br][br]-=-=-=-=- 以下内容由 申一言 在 时添加 -=-=-=-=-
所谓雕琢就是拼凑也！？
但是纯粹数学不是拼凑数学！
是结构数学！是抽象数学！

ysr

太脱离实际的东西才最可能是假的，假作真时真亦假