感谢dlpangong网友提供的一万亿以内的素数

柳林 · 发表于 2018-6-29 16:58

区间密度近似值实际值素数误差误差率
N Mn N*Mn+1

21 33.333333333 8.00 8 19 0.00 0.0000
84 26.666666667 23.40 23 83 0.40 1.7391
189 22.857142857 44.20 42 181 2.20 5.2381
336 20.779220779 70.82 67 331 3.82 5.6988
525 19.180819181 101.70 99 523 2.70 2.7266
756 18.052535700 137.48 133 751 4.48 3.3663
1029 17.102402242 176.98 172 1021 4.98 2.8975
1344 16.358819536 220.86 217 1327 3.86 1.7800
1701 15.794722310 269.67 266 1699 3.67 1.3790
2100 15.285215139 321.99 317 2099 4.99 1.5740
2541 14.872101216 378.90 371 2539 7.90 2.1294
3024 14.509367040 439.76 434 3023 5.76 1.3279
3549 14.171939900 503.96 497 3547 6.96 1.4008
4116 13.870409264 571.91 566 4111 5.91 1.0435
4725 13.608703428 644.01 637 4723 7.01 1.1007
5376 13.378047438 720.20 708 5351 12.20 1.7237
6069 13.158735185 799.60 791 6067 8.60 1.0877
6804 12.962336152 882.96 876 6803 6.96 0.7942
7581 12.779768038 969.83 962 7577 7.83 0.8144
8400 12.604702722 1059.80 1051 8389 8.80 0.8368
9261 12.445149523 1153.55 1147 9257 6.55 0.5706

柳林 · 发表于 2018-6-29 17:00

区间       密度                近似值       实际值       素数       误差       误差率

10164 12.295207962 1250.68 1248          10163 2.68 0.2151
11109 12.157059558 1351.53 1345          11093 6.53 0.4853
12096 12.031729047 1456.36 1446          12073 10.36 0.7163
13125 11.912603017 1564.53 1561 13121 3.53 0.2261
14196 11.796946677 1675.69 1669 14177 6.69 0.4011
15309 11.686694839 1790.12 1788 15307 2.12 0.1184
16464 11.579477455 1907.45 1908 16453 -0.55 -0.0291
17661 11.477004204 2027.95 2029 17659 -1.05 -0.0516
18900 11.386634092 2153.07 2150 18899 3.07 0.1430
20181 11.299713221 2281.40 2283 20177 -1.60 -0.0703
21504 11.217233562 2413.15 2413 21503 0.15 0.0064
22869 11.136534040 2547.81 2553 22861 -5.19 -0.2031
24276 11.061792201 2686.36 2699 24251 -12.64 -0.4683
25725 10.988535299 2827.80 2832 25717 -4.20 -0.1483
27216 10.918544628 2972.59 2980 27211 -7.41 -0.2486
28749 10.851559692 3120.71 3130 28729 -9.29 -0.2966
30324 10.786580293 3271.92 3279 30323 -7.08 -0.2158
31941 10.724230118 3426.43 3427 31907 -0.57 -0.0167
33600 10.664318217 3584.21 3598 33599 -13.79 -0.3832
35301 10.605399332 3744.81 3760 35291 -15.19 -0.4039
37044 10.549873681 3909.10 3928 37039 -18.90 -0.4813
38829 10.495211123 4076.19 4090 38821 -13.81 -0.3378
40656 10.441935940 4246.27 4260 40639 -13.73 -0.3222
42525 10.389463900 4419.12 4448 42509 -28.88 -0.6493
44436 10.340224735 4595.78 4619 44417 -23.22 -0.5027
46389 10.293856014 4776.22 4795 46381 -18.78 -0.3917
48384 10.248508631 4959.64 4977 48383 -17.36 -0.3488
50421 10.203755318 5145.84 5174 50417 -28.16 -0.5443
52500 10.159962377 5334.98 5359 52489 -24.02 -0.4482
54621 10.117452074 5527.25 5558 54617 -30.75 -0.5532
56784 10.075470945 5722.26 5758 56783 -35.74 -0.6208
58989 10.035329626 5920.74 5961 58979 -40.26 -0.6754
61236 9.996281651 6122.32 6163 61231 -40.68 -0.6600
63525 9.958272976 6326.99 6366 63521 -39.01 -0.6127
65856 9.921253373 6534.74 6579 65851 -44.26 -0.6727
68229 9.884643582 6745.19 6792 68227 -46.81 -0.6891
70644 9.848958948 6958.70 6999 70639 -40.30 -0.5758
73101 9.813909273 7175.07 7228 73091 -52.93 -0.7323
75600 9.779231148 7394.10 7447 75583 -52.90 -0.7104
78141 9.745854932 7616.51 7673 78139 -56.49 -0.7362
80724 9.714109477 7842.62 7900 80713 -57.38 -0.7264
83349 9.682874398 8071.58 8136 83341 -64.42 -0.7918
86016 9.651938697 8303.21 8363 86011 -59.79 -0.7149
88725 9.621490941 8537.67 8592 88721 -54.33 -0.6324
91476 9.592422992 8775.76 8846 91463 -70.24 -0.7940
94269 9.563958829 9016.85 9091 94261 -74.15 -0.8157
97104 9.536396988 9261.22 9344 97103 -82.78 -0.8859
99981 9.509072068 9508.27 9590 99971 -81.73 -0.8523
102900 9.482134187 9758.12 9846 102881 -87.88 -0.8926
105861 9.455721557 10010.92 10092 105829 -81.08 -0.8034
108864 9.429956648 10266.83 10347 108863 -80.17 -0.7748
111909 9.404675263 10525.68 10612 111893 -86.32 -0.8134
114996 9.379860817 10787.46 10870 114973 -82.54 -0.7593
118125 9.355370318 11052.03 11143 118093 -90.97 -0.8164
121296 9.331320523 11319.52 11413 121291 -93.48 -0.8191
124509 9.307815937 11590.07 11693 124493 -102.93 -0.8803
127764 9.284604426 11863.38 11969 127763 -105.62 -0.8824
131061 9.261903682 12139.74 12249 131059 -109.26 -0.8920
134400 9.239798900 12419.29 12533 134399 -113.71 -0.9073
137781 9.217851634 12701.45 12823 137777 -121.55 -0.9479
141204 9.196464507 12986.78 13112 141199 -125.22 -0.9550
144669 9.175225559 13274.71 13395 144667 -120.29 -0.8980
148176 9.154325273 13565.51 13688 148171 -122.49 -0.8948
151725 9.133660882 13859.05 14001 151717 -141.95 -1.0139
155316 9.113318653 14155.44 14298 155303 -142.56 -0.9970
158949 9.093377037 14454.83 14595 158941 -140.17 -0.9604
162624 9.073651707 14756.94 14897 162623 -140.06 -0.9402
166341 9.054054187 15061.60 15198 166319 -136.40 -0.8975
170100 9.034666491 15368.97 15505 170099 -136.03 -0.8773
173901 9.015804974 15679.58 15825 173897 -145.42 -0.9190
177744 8.997292028 15993.15 16137 177743 -143.85 -0.8914
181629 8.978967604 16309.41 16460 181619 -150.59 -0.9149
185556 8.960973681 16628.62 16793 185551 -164.38 -0.9788
189525 8.943158624 16950.52 17128 189523 -177.48 -1.0362
193536 8.925588568 17275.23 17457 193513 -181.77 -1.0413
197589 8.908456920 17603.13 17785 197573 -181.87 -1.0226
201684 8.891423541 17933.58 18116 201683 -182.42 -1.0070
205821 8.874988378 18267.59 18449 205817 -181.41 -0.9833
210000 8.858763536 18604.40 18807 209987 -202.60 -1.0772
214221 8.842859113 18944.26 19149 214219 -204.74 -1.0692
218484 8.827152436 19286.92 19481 218479 -194.08 -0.9963
222789 8.811638987 19632.36 19837 222787 -204.64 -1.0316
227136 8.796207045 19980.35 20189 227131 -208.65 -1.0335
231525 8.780962319 20331.12 20561 231503 -229.88 -1.1180
235956 8.766003269 20684.91 20903 235951 -218.09 -1.0433
240429 8.751220801 21041.47 21256 240421 -214.53 -1.0093
244944 8.736611084 21400.80 21631 244943 -230.20 -1.0642
249501 8.722074293 21762.66 22004 249499 -241.34 -1.0968
254100 8.707705143 22127.28 22371 254083 -243.72 -1.0895
258741 8.693500077 22494.65 22742 258737 -247.35 -1.0876
263424 8.679410126 22864.65 23102 263423 -237.35 -1.0274
268149 8.665388462 23237.15 23498 268133 -260.85 -1.1101
272916 8.651655675 23612.75 23878 272911 -265.25 -1.1108
277725 8.638158552 23991.33 24258 277703 -266.67 -1.0993
282576 8.624724402 24372.40 24647 282571 -274.60 -1.1141
287469 8.611394071 24756.09 25029 287449 -272.91 -1.0904
292404 8.598206637 25142.50 25415 292393 -272.50 -1.0722
297381 8.585159283 25531.63 25797 297377 -265.37 -1.0287
302400 8.572171144 25923.25 26187 302399 -263.75 -1.0072
307461 8.559433892 26317.92 26609 307451 -291.08 -1.0939
312564 8.546790710 26715.19 26998 312563 -282.81 -1.0475
317709 8.534277107 27115.17 27414 317701 -298.83 -1.0901
322896 8.521926489 27517.96 27839 322891 -321.04 -1.1532
328125 8.509769675 27923.68 28261 328121 -337.32 -1.1936
333396 8.497767179 28332.22 28670 333383 -337.78 -1.1782
338709 8.485948310 28743.67 29095 338707 -351.33 -1.2075
344064 8.474275754 29157.93 29504 344053 -346.07 -1.1730
349461 8.462714668 29574.89 29932 349423 -357.11 -1.1931
354900 8.451263092 29994.53 30369 354883 -374.47 -1.2331
360381 8.439888579 30416.75 30785 360337 -368.25 -1.1962
365904 8.428650379 30841.77 31213 365903 -371.23 -1.1893
371469 8.417516098 31269.46 31631 371453 -361.54 -1.1430
377076 8.406454973 31699.72 32074 377071 -374.28 -1.1669
382725 8.395523302 32132.77 32499 382709 -366.23 -1.1269
388416 8.384662341 32568.37 32941 388403 -372.63 -1.1312
394149 8.374008386 33007.07 33409 394129 -401.93 -1.2031
399924 8.363501475 33448.65 33854 399913 -405.35 -1.1973
405741 8.353163401 33893.21 34283 405731 -389.79 -1.1370
411600 8.342863569 34340.23 34736 411589 -395.77 -1.1394
417501 8.332701738 34790.11 35188 417493 -397.89 -1.1307
423444 8.322576949 35242.45 35655 423439 -412.55 -1.1571
429429 8.312513373 35697.34 36106 429427 -408.66 -1.1318
435456 8.302486216 36154.67 36603 435451 -448.33 -1.2248
441525 8.292590523 36614.86 37059 441523 -444.14 -1.1985
447636 8.282868846 37078.10 37529 447617 -450.90 -1.2015
453789 8.273203888 37543.89 37992 453757 -448.11 -1.1795
459984 8.263572685 38012.11 38458 459961 -445.89 -1.1594
466221 8.253997282 38482.87 38932 466201 -449.13 -1.1536
472500 8.244585654 38956.67 39426 472477 -469.33 -1.1904
478821 8.235227441 39433.00 39916 478813 -483.00 -1.2100
485184 8.225901023 39911.76 40397 485171 -485.24 -1.2012
491589 8.216627177 40393.04 40888 491581 -494.96 -1.2105
498036 8.207568051 40877.64 41386 498013 -508.36 -1.2283
504525 8.198558646 41364.78 41873 504523 -508.22 -1.2137
511056 8.189637473 41854.63 42368 511039 -513.37 -1.2117
517629 8.180821932 42347.31 42883 517619 -535.69 -1.2492
524244 8.172091065 42842.70 43386 524243 -543.30 -1.2523
530901 8.163406590 43340.61 43899 530897 -558.39 -1.2720
537600 8.154786309 43841.13 44397 537599 -555.87 -1.2520
544341 8.146229345 44344.27 44903 544279 -558.73 -1.2443
551124 8.137805116 44850.40 45412 551113 -561.60 -1.2367
557949 8.129424266 45359.04 45919 557927 -559.96 -1.2194
564816 8.121103464 45870.29 46432 564797 -561.71 -1.2097
571725 8.112841914 46384.15 46954 571721 -569.85 -1.2136
578676 8.104655393 46900.70 47486 578659 -585.30 -1.2326
585669 8.096526351 47419.84 48013 585653 -593.16 -1.2354
592704 8.088502043 47941.88 48547 592693 -605.12 -1.2465
599781 8.080517342 48466.41 49082 599779 -615.59 -1.2542
606900 8.072587492 48993.53 49617 606899 -623.47 -1.2566
614061 8.064680942 49523.06 50162 614051 -638.94 -1.2738
621264 8.056858749 50055.36 50708 621259 -652.64 -1.2870
628509 8.049059273 50590.06 51233 628499 -642.94 -1.2549
635796 8.041312344 51127.34 51776 635777 -648.66 -1.2528
643125 8.033646651 51667.39 52302 643121 -634.61 -1.2134
650496 8.026002838 52209.83 52859 650483 -649.17 -1.2281
657909 8.018438274 52755.03 53405 657893 -649.97 -1.2171
665364 8.010895058 53302.61 53978 665359 -675.39 -1.2512
672861 8.003401237 53852.77 54523 672827 -670.23 -1.2293
680400 7.996038402 54406.05 55095 680399 -688.95 -1.2505
687981 7.988709311 54961.80 55662 687977 -700.20 -1.2579
695604 7.981400337 55519.94 56229 695603 -709.06 -1.2610
703269 7.974124675 56080.55 56790 703267 -709.45 -1.2493
710976 7.966895188 56643.71 57381 710971 -737.29 -1.2849
718725 7.959711333 57209.44 57938 718723 -728.56 -1.2575
726516 7.952585360 57777.81 58525 726497 -747.19 -1.2767
734349 7.945503806 58348.73 59105 734347 -756.27 -1.2795
742224 7.938466159 58922.20 59689 742219 -766.80 -1.2847
750141 7.931569142 59498.95 60249 750137 -750.05 -1.2449
758100 7.924690071 60078.08 60829 758099 -750.92 -1.2345
766101 7.917876064 60659.93 61443 766097 -783.07 -1.2745
774144 7.911114428 61244.42 62044 774143 -799.58 -1.2887
782229 7.904415770 61831.63 62641 782219 -809.37 -1.2921
790356 7.897756616 62421.39 63233 790351 -811.61 -1.2835
798525 7.891136535 63013.70 63851 798521 -837.30 -1.3113
806736 7.884566064 63608.63 64448 806719 -839.37 -1.3024
814989 7.878066009 64206.37 65051 814949 -844.63 -1.2984
823284 7.871592660 64806.56 65668 823283 -861.44 -1.3118
831621 7.865156362 65409.29 66282 831619 -872.71 -1.3167
840000 7.858756723 66014.56 66890 839999 -875.44 -1.3088
848421 7.852372680 66622.18 67499 848417 -876.82 -1.2990
856884 7.846024763 67232.33 68116 856853 -883.67 -1.2973
865389 7.839742918 67845.27 68750 865379 -904.73 -1.3160
873936 7.833515958 68460.92 69369 873913 -908.08 -1.3091
882525 7.827381646 69079.60 70010 882517 -930.40 -1.3290
891156 7.821261723 69700.64 70634 891151 -933.36 -1.3214
899829 7.815165650 70324.13 71262 899807 -937.87 -1.3161
908544 7.809102682 70950.13 71906 908543 -955.87 -1.3293
917301 7.803053803 71578.49 72535 917291 -956.51 -1.3187
926100 7.797037571 72209.36 73194 926099 -984.64 -1.3452
934941 7.791044459 72842.67 73832 934939 -989.33 -1.3400
943824 7.785065147 73478.31 74477 943819 -998.69 -1.3409
952749 7.779108708 74116.38 75109 952741 -992.62 -1.3216
961716 7.773210976 74757.21 75748 961703 -990.79 -1.3080
970725 7.767326638 75400.38 76400 970721 -999.62 -1.3084
979776 7.761473340 76046.05 77054 979757 -1007.95 -1.3081
988869 7.755770567 76695.41 77698 988861 -1002.59 -1.2904
998004 7.750096997 77347.28 78359 997991 -1011.72 -1.2911

柳林 · 发表于 2018-6-29 17:03

区间密度近似值实际值素数误差误差率

1007181 7.744452352 78001.65 79035 1007179 -1033.35 -1.3075
1016400 7.738844494 78658.62 79713 1016399 -1054.38 -1.3227
1025661 7.733312797 79318.57 80391 1025659 -1072.43 -1.3340
1034964 7.727824285 79981.20 81057 1034959 -1075.80 -1.3272
1044309 7.722393629 80646.65 81723 1044299 -1076.35 -1.3171
1053696 7.716982000 81314.53 82383 1053691 -1068.47 -1.2970
1063125 7.711581733 81984.75 83044 1063123 -1059.25 -1.2755
1072596 7.706200308 82657.40 83730 1072543 -1072.60 -1.2810
1082109 7.700845061 83332.54 84431 1082099 -1098.46 -1.3010
1091664 7.695523123 84010.26 85110 1091663 -1099.74 -1.2921
1101261 7.690219523 84690.39 85800 1101253 -1109.61 -1.2933
1110900 7.684926874 85372.85 86513 1110887 -1140.15 -1.3179
1120581 7.679659617 86057.81 87211 1120577 -1153.19 -1.3223
1130304 7.674438911 86745.49 87905 1130299 -1159.51 -1.3190
1140069 7.669256980 87435.82 88602 1139993 -1166.18 -1.3162
1149876 7.664085532 88128.48 89290 1149859 -1161.52 -1.3008
1159725 7.658931474 88823.54 90012 1159721 -1188.46 -1.3203
1169616 7.653787799 89520.93 90741 1169603 -1220.07 -1.3446
1179549 7.648661350 90220.71 91456 1179547 -1235.29 -1.3507
1189524 7.643558841 90922.97 92187 1189483 -1264.03 -1.3712
1199541 7.638500232 91627.94 92900 1199521 -1272.06 -1.3693
1209600 7.633484802 92335.63 93587 1209587 -1251.37 -1.3371
1219701 7.628498855 93045.88 94323 1219679 -1277.12 -1.3540
1229844 7.623554915 93758.83 95040 1229827 -1281.17 -1.3480
1240029 7.618633317 94474.26 95750 1240027 -1275.74 -1.3324
1250256 7.613727565 95192.09 96489 1250243 -1296.91 -1.3441
1260525 7.608843840 95912.38 97218 1260509 -1305.62 -1.3430
1270836 7.603988164 96635.22 97964 1270823 -1328.78 -1.3564
1281189 7.599147942 97360.45 98687 1281187 -1326.55 -1.3442
1291584 7.594335309 98088.22 99440 1291579 -1351.78 -1.3594
1302021 7.589537877 98818.38 100168 1302019 -1349.62 -1.3474
1312500 7.584785505 99551.31 100909 1312471 -1357.69 -1.3455
1323021 7.580047975 100286.63 101664 1323017 -1377.37 -1.3548
1333584 7.575331081 101024.40 102397 1333583 -1372.60 -1.3405
1344189 7.570622982 101764.48 103160 1344181 -1395.52 -1.3528
1354836 7.565929478 102506.94 103889 1354823 -1382.06 -1.3303
1365525 7.561256266 103251.84 104654 1365503 -1402.16 -1.3398
1376256 7.556591704 103999.05 105407 1376237 -1407.95 -1.3357
1387029 7.551947210 104748.70 106182 1387021 -1433.30 -1.3499
1397844 7.547333925 105500.95 106951 1397839 -1450.05 -1.3558
1408701 7.542779106 106256.20 107715 1408699 -1458.80 -1.3543
1419600 7.538243461 107013.90 108458 1419589 -1444.10 -1.3315
1430541 7.533721419 107773.97 109234 1430521 -1460.03 -1.3366
1441524 7.529207506 108536.33 110034 1441523 -1497.67 -1.3611
1452549 7.524760248 109301.83 110810 1452541 -1508.17 -1.3610
1463616 7.520326093 110069.70 111602 1463611 -1532.30 -1.3730
1474725 7.515899768 110839.85 112373 1474721 -1533.15 -1.3643
1485876 7.511501933 111612.60 113161 1485871 -1548.40 -1.3683
1497069 7.507137319 112388.03 113967 1497061 -1578.97 -1.3855
1508304 7.502780303 113165.74 114763 1508303 -1597.26 -1.3918
1519581 7.498450944 113946.04 115559 1519561 -1612.96 -1.3958
1530900 7.494143964 114728.85 116339 1530871 -1610.15 -1.3840
1542261 7.489854243 115514.10 117128 1542259 -1613.90 -1.3779
1553664 7.485581650 116301.79 117921 1553653 -1619.21 -1.3731
1565109 7.481326061 117091.91 118720 1565099 -1628.09 -1.3714
1576596 7.477115973 117884.91 119525 1576583 -1640.09 -1.3722
1588125 7.472922414 118680.35 120312 1588121 -1631.65 -1.3562
1599696 7.468740588 119478.14 121110 1599691 -1631.86 -1.3474
1611309 7.464565775 120278.22 121945 1611307 -1666.78 -1.3668
1622964 7.460421097 121080.95 122747 1622953 -1666.05 -1.3573
1634661 7.456301593 121886.25 123588 1634657 -1701.75 -1.3770
1646400 7.452211466 122694.21 124391 1646387 -1696.79 -1.3641
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4899069 6.880450009 337078.99 341927 4899067 -4848.01 -1.4178
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4960116 6.874496916 340984.02 345881 4960097 -4896.98 -1.4158
4980549 6.872527710 342290.61 347247 4980539 -4956.39 -1.4273

柳林 · 发表于 2018-6-29 17:05

区间密度近似值实际值素数误差误差率

5001024 6.870563569 343599.53 348579 5001023 -4979.47 -1.4285
5021541 6.868606701 344910.90 349895 5021537 -4984.10 -1.4245
5042100 6.866653728 346224.55 351224 5042099 -4999.45 -1.4234
5062701 6.864706846 347540.58 352557 5062697 -5016.42 -1.4229
5083344 6.862761619 348858.78 353891 5083343 -5032.22 -1.4220
5104029 6.860819144 350179.20 355228 5104013 -5048.80 -1.4213
5124756 6.858880512 351501.89 356568 5124683 -5066.11 -1.4208
5145525 6.856943523 352826.74 357917 5145521 -5090.26 -1.4222
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5187189 6.853083167 355483.38 360584 5187181 -5100.62 -1.4145
5208084 6.851157603 356815.04 361953 5208079 -5137.96 -1.4195
5229021 6.849239048 358149.15 363300 5229011 -5150.85 -1.4178
5250000 6.847326387 359485.64 364685 5249989 -5199.36 -1.4257
5271021 6.845415328 360824.28 366038 5270987 -5213.72 -1.4244
5292084 6.843510119 362165.30 367391 5292071 -5225.70 -1.4224
5313189 6.841612833 363508.82 368747 5313181 -5238.18 -1.4205
5334336 6.839719223 364854.60 370122 5334331 -5267.40 -1.4232
5355525 6.837828231 366202.60 371485 5355503 -5282.40 -1.4220
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5398029 6.834058231 368905.45 374229 5397979 -5323.55 -1.4225
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5462100 6.828437054 372977.06 378370 5462089 -5392.94 -1.4253
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5898900 6.792032073 400656.18 406355 5898859 -5698.82 -1.4024
5921181 6.790260085 402064.59 407823 5921177 -5758.41 -1.4120
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6169044 6.771049000 417709.99 423684 6169039 -5974.01 -1.4100
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9998100 6.553186607 655195.15 664465 9998099 -9269.85 -1.3951

柳林 · 发表于 2018-6-29 17:17

区间密度近似值实际值素数误差误差率
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11812500 6.481524501 765631.08 776536 11812459 -10904.92 -1.4043
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柳林 · 发表于 2018-6-29 17:18

区间密度近似值实际值素数误差误差率

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柳林 · 发表于 2018-6-29 17:28

区间密度近似值实际值素数误差误差率

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934266900 5.051473791 47194248.59 47683766 934547051 -489517.41 -1.0266
937070400 5.050719962 47328802.75 47819499 937350977 -490696.25 -1.0261
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951150900 5.046969906 48004300.69 48500605 951433579 -496304.31 -1.0233
953979600 5.046223473 48139943.50 48637650 954262697 -497706.50 -1.0233
956812500 5.045478596 48275770.89 48774604 957096001 -498833.11 -1.0227
959649600 5.044734775 48411778.08 48912131 959933519 -500352.92 -1.0230
962490900 5.043992241 48547967.32 49049599 962775257 -501631.68 -1.0227
965336400 5.043250954 48684338.20 49187285 965621159 -502946.80 -1.0225
968186100 5.042511188 48820893.42 49324912 968471261 -504018.58 -1.0218
971040000 5.041772989 48957633.43 49462898 971325613 -505264.57 -1.0215
973898100 5.041036569 49094560.37 49600917 974184139 -506356.63 -1.0209
976760400 5.040301234 49231667.50 49739058 977046803 -507390.50 -1.0201
979626900 5.039567424 49368959.13 49877433 979913777 -508473.87 -1.0194
982497600 5.038834750 49506431.49 50016052 982784893 -509620.51 -1.0189
985372500 5.038103436 49644086.78 50155290 985660211 -511203.22 -1.0192
988251600 5.037373453 49781924.75 50294245 988539737 -512320.25 -1.0186
991134900 5.036644943 49919946.82 50433616 991423457 -513669.18 -1.0185
994022400 5.035917605 50058150.04 50572889 994311379 -514738.96 -1.0178
996914100 5.035191752 50196537.54 50712546 997203469 -516008.46 -1.0175
999810000 5.034466990 50335105.41 50852354 1000099799 -517248.59 -1.0172

柳林 · 发表于 2018-6-29 17:34

区间       密度                近似值          实际值          素数                   误差率

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1026062100 5.028006006 51590465.01 52118799 1026355697 -1.0137
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1031942100 5.026583452 51871431.83 52402127 1032236539 -1.0127
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1043752500 5.023752800 52435546.45 52971355 1044048589 -1.0115
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1097730900 5.011237231 55009900.56 55568004 1098034577 -1.0044
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1171818900 4.995125153 58533821.63 59121379 1172132653 -0.9938
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1178102100 4.993810428 58832186.52 59422080 1178416699 -0.9927
1181250000 4.993154680 58981640.66 59572740 1181565013 -0.9922
1184402100 4.992500054 59131276.48 59723483 1184717519 -0.9916
1187558400 4.991846620 59281094.86 59874528 1187874227 -0.9911
1190718900 4.991194206 59431093.75 60025737 1191035179 -0.9906
1193883600 4.990542838 59581273.49 60177076 1194200281 -0.9901
1197052500 4.989892614 59731635.28 60328783 1197369601 -0.9898
1200225600 4.989243442 59882178.03 60480507 1200543119 -0.9893
1203402900 4.988595356 60032902.18 60632373 1203720841 -0.9887
1206584400 4.987948389 60183808.14 60784572 1206902737 -0.9883
1209770100 4.987302544 60334895.97 60937016 1210088881 -0.9881
1212960000 4.986657512 60486161.95 61089544 1213279213 -0.9877
1216154100 4.986013502 60637608.64 61242317 1216473737 -0.9874
1219352400 4.985370391 60789234.51 61395371 1219672457 -0.9873
1222554900 4.984728000 60941037.41 61548350 1222875371 -0.9867
1225761600 4.984086512 61093019.57 61701417 1226082497 -0.9860
1228972500 4.983445843 61245179.96 61854527 1229293781 -0.9851
1232187600 4.982806373 61397523.26 62008423 1232509319 -0.9852
1235406900 4.982168001 61550048.25 62162115 1235729059 -0.9846
1238630400 4.981530689 61702754.50 62316143 1238952959 -0.9843
1241858100 4.980894318 61855640.54 62470202 1242181097 -0.9838
1245090000 4.980259191 62008710.17 62624323 1245413383 -0.9830
1248326100 4.979625110 62161960.93 62779180 1248649907 -0.9832
1251566400 4.978991965 62315391.49 62934054 1251890623 -0.9830
1254810900 4.978359923 62469003.96 63089079 1255135579 -0.9829
1258059600 4.977728779 62622795.76 63243758 1258384667 -0.9819
1261312500 4.977098784 62776770.10 63399181 1261637989 -0.9817
1264569600 4.976469973 62930927.43 63554517 1264895507 -0.9812
1267830900 4.975842055 63085264.10 63710489 1268157251 -0.9814
1271096400 4.975215046 63239780.35 63866477 1271423177 -0.9813
1274366100 4.974588942 63394476.10 64022468 1274693263 -0.9809
1277640000 4.973963957 63549354.10 64178375 1277967619 -0.9801
1280918100 4.973339761 63704410.17 64334870 1281246067 -0.9800
1284200400 4.972716667 63859648.33 64491306 1284528841 -0.9794
1287486900 4.972094280 64015063.51 64647975 1287815779 -0.9790
1290777600 4.971472868 64170659.17 64804990 1291106881 -0.9788
1294072500 4.970852556 64326436.94 64962034 1294402217 -0.9784
1297371600 4.970233029 64482392.78 65118875 1297701737 -0.9774
1300674900 4.969614359 64638527.59 65276369 1301005429 -0.9771
1303982400 4.968996816 64794844.94 65433941 1304313379 -0.9767
1307294100 4.968380351 64951344.20 65591821 1307625497 -0.9765
1310610000 4.967764631 65108021.02 65750273 1310941777 -0.9768
1313930100 4.967149702 65264876.05 65908200 1314262337 -0.9761
1317254400 4.966535645 65421910.32 66066334 1317587041 -0.9754
1320582900 4.965922483 65579124.14 66224917 1320915971 -0.9752
1323915600 4.965309990 65736514.55 66383377 1324249093 -0.9744
1327252500 4.964698427 65894085.00 66542334 1327586419 -0.9742
1330593600 4.964087856 66051836.31 66701200 1330927907 -0.9735
1333938900 4.963478202 66209767.53 66860752 1334273657 -0.9736
1337288400 4.962869615 66367880.67 67020370 1337623543 -0.9736
1340642100 4.962261890 66526173.01 67179784 1340977699 -0.9729
1344000000 4.961654950 66684643.53 67339911 1344336001 -0.9731
1347362100 4.961049069 66843295.91 67499844 1347698533 -0.9727
1350728400 4.960443931 67002125.94 67659996 1351065229 -0.9723
1354098900 4.959839568 67161134.03 67820357 1354436179 -0.9720
1357473600 4.959236154 67320322.55 67981116 1357811297 -0.9720
1360852500 4.958633469 67479688.52 68141822 1361190617 -0.9717
1364235600 4.958031832 67639236.31 68302744 1364574121 -0.9714
1367622900 4.957431035 67798963.09 68463750 1367961857 -0.9710
1371014400 4.956830976 67958867.47 68625049 1371353779 -0.9708
1374410100 4.956231957 68118953.59 68786149 1374749879 -0.9700
1377810000 4.955633747 68279218.33 68947435 1378150219 -0.9692
1381214100 4.955036667 68439666.11 69109290 1381554721 -0.9689
1384622400 4.954440517 68600294.20 69271131 1384963453 -0.9684
1388034900 4.953845331 68761103.09 69433183 1388376373 -0.9680
1391451600 4.953251015 68922091.50 69595886 1391793497 -0.9682
1394872500 4.952657427 69083257.47 69758274 1395214817 -0.9677
1398297600 4.952064828 69244604.65 69920838 1398640319 -0.9671
4179748944 4.701679206 196518387.96 198108916 4180341457 -0.8029
4185676404 4.701372021 196784220.36 198376427 4186269341 -0.8026
4191608064 4.701065162 197050227.41 198644187 4192201423 -0.8024
4197543924 4.700758581 197316407.21 198912164 4198137739 -0.8022
4203483984 4.700452233 197582757.80 199180632 4204078201 -0.8022
4209428244 4.700146091 197849278.04 199448994 4210022897 -0.8021
4215376704 4.699840242 198115971.69 199717517 4215971777 -0.8019
4221329364 4.699534708 198382839.61 199985820 4221924853 -0.8015
4227286224 4.699229460 198649880.59 200254570 4227882107 -0.8013
4233247284 4.698924457 198917092.96 200523552 4233843553 -0.8011
4239212544 4.698619682 199184475.96 200792550 4239809269 -0.8009
4245182004 4.698315154 199452030.42 201061815 4245779179 -0.8006
4251155664 4.698010861 199719755.83 201331433 4251753239 -0.8005
4257133524 4.697706880 199987655.46 201600912 4257731539 -0.8002
4263115584 4.697403150 200255726.74 201870576 4263714017 -0.7999
4269101844 4.697099657 200523969.07 202140577 4269700697 -0.7997
4275092304 4.696796410 200792382.84 202410948 4275691571 -0.7996
4281086964 4.696493432 201060969.08 202681766 4281686627 -0.7997
4287085824 4.696190728 201329727.98 202952271 4287685933 -0.7995
4293088884 4.695888263 201598658.02 203222894 4293689401 -0.7992
5328393861 4.649715931 247755179.21   249638331 5328393861 -0.7544
6888935424 4.596041832 316618354.84   318902774 6888935424 -0.7163
8648775156 4.549569075 393482000.85   396187685 8648775156 -0.6829
10608582096 4.508677042 478306706.47   481446295 10608582096 -0.6521
12768356244 4.472238789 571031381.61   574619307 12768356244 -0.6244
15128097600 4.439444575 671603509.21   675647352 15128097600 -0.5985
17687806164 4.409642199 779968965.60   784477377 17687806164 -0.5747
20448792525 4.382350653 896137793.69   901119407 20448792525 -0.5528
23408527149 4.357247563 1019967479.69 1025424367 23408527149 -0.5322
26568228981 4.334009508 1151469571.26  1157403625 26568228981 -0.5127
29927898021 4.312385323 1290606282.89  1297018227 29927898021 -0.4944
33487534269 4.292188020 1437347935.23  1444237688 33487534269 -0.4771
37248906576 4.273233231 1591732654.88  1599100694 37248906576 -0.4608
41208568884 4.255402619 1753590520.56  1761428366 41208568884 -0.4450
45368198400 4.238576928 1922965991.09  1931276872 45368198400 -0.4303
49727795124 4.222652793 2099832130.54  2108602147 49727795124 -0.4159
54287359056 4.207538808 2284161701.37  2293396312 54287359056 -0.4027
59046890196 4.193171619 2475937442.78  2485620602 59046890196 -0.3896
64008707301 4.179476132 2675228644.90  2685350357 64008707301 -0.3769
69168264501 4.166403699 2881829131.62  2892383316 69168264501 -0.3649
74527788909 4.153897610 3095808043.41  3106782005 74527788909 -0.3532
80087280525 4.141919027 3317150311.29  3328535550 80087280525 -0.3420
85846739349 4.130421917 3545832538.29  3557618779 85846739349 -0.3313
91808942400 4.119367370 3781947616.81  3794120304 91808942400 -0.3208
97968427284 4.108735346 4025263401.01  4037813451 97968427284 -0.3108
1.444E+11             4.046396305 5842996265.44 5857663250 1.444E+11 -0.2504
2.304E+11          3.973891390 9155845764.27 9172116737 2.304E+11 -0.1774
7.396E+11    3.804192273 28135806053.65 28134510924 7.396E+11 0.0046
9.216E+11       3.773857241 34779868333.17 34766377806 9.216E+11 0.0388
9.409E+11          3.771025613 35481579989.67 35466674593 9.409E+11 0.0420
9.60404E+11 3.768226188 36190202564.38 36173704275 9.604E+11 0.0456
9.80112E+11 3.765459612 36905709942.72 36887443015 9.801E+11 0.0495
1E+12          3.762727372 37627273723.85 37607912018 1E+12 0.0515
1E+16    2.8312500279 283125002179911.00  279238341033925 1E+16    1.3919

柳林 · 发表于 2018-6-30 12:17

这个计算结果比高斯的素数定理精确得多。可惜当年欧拉没有找到21n^2这个计算区间。否则，素数定理就属于欧拉的了。

ysr · 发表于 2018-7-1 11:06

精确，不过我喜欢的是下限公式，只要界限是明确的，不管误差多大，一般误差是随着函数增长而增大这样就保证他始终都是下限公式。这样公式才能得到明确结论，否则结果就是大致如此，象某些人用“高等数学”得出的结论，岂不是白忙活了？

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