特大偶数强哥猜数的估算

重生888@ · 发表于 2022-9-24 18:54

创新与学历无因果关系！有个故事，从1+2+3.....+.50....+100=？小学生也有创新之举！

yangchuanju · 发表于 2022-9-25 19:22

独木星空谁发表于 2022-9-23 20:20
数字 9999999967
该数性质 9999999967
因式分解 9999999967

白新岭用素数个数的平方求哥猜的公式精确度相当高！
公式简介如下：
r2(x)=综合调整系数*(x内素数个数-x平方根内素数个数)^2/x=2c*k*[π(x)-π(x^0.5)]^2/x
式中：c——哈李常数或称孪生素数常数，c=0.6601618158…；k——波动因子，k=∏(p-1)/(p-2)，3≤p≤x^0.5，p|x
请看以下两表，不足之处是计算公式必须带入偶数x以内及x平方根以内的真实素数个数值，不能带入根据素数定理计算的素数个数值。

yangchuanju · 发表于 2022-9-25 19:23

本帖最后由 yangchuanju 于 2022-9-25 22:04 编辑

x π(x) x^2 π(x^2) 波动因子白平方式计算值哥猜数真值白/哥
1000 168 1000000 78498 1.33333 5400.6 5402 0.99975
2000 303 4000000 283146 1.33333 17604.4 17638 0.99809
3000 430 9000000 602489 2.66667 70901.4 70619 1.00400
4000 550 16000000 1031130 1.33333 58429.6 58383 1.00080
5000 669 25000000 1565927 1.33333 86262.3 85838 1.00494
6000 783 36000000 2204262 2.66667 237429.4 237050 1.00160
7000 900 49000000 2944531 1.60000 186784.6 186553 1.00124
8000 1007 64000000 3785086 1.33333 196938.0 196600 1.00172
9000 1117 81000000 4724409 2.66667 484868.2 484222 1.00133
10000 1229 100000000 5761455 1.33333 292057.4 291400 1.00226
11000 1335 121000000 6895267 1.48148 384145.1 383146 1.00261
12000 1438 144000000 8125404 2.66667 806850.1 804830 1.00251
13000 1547 169000000 9450213 1.45455 507261.6 505820 1.00285
14000 1652 196000000 10869898 1.60000 636551.0 635368 1.00186
15000 1754 225000000 12382875 2.66667 1199379.3 1197257 1.00177
16000 1862 256000000 13989537 1.33333 672729.1 671244 1.00221
17000 1960 289000000 15688229 1.42222 799391.1 798100 1.00162
18000 2064 324000000 17479433 2.66667 1659687.2 1656506 1.00192
19000 2158 361000000 19361840 1.41176 967613.6 966507 1.00114
20000 2262 400000000 21336326 1.33333 1001558.5 999700 1.00186
21000 2360 441000000 23400956 3.20000 2622656.3 2617879 1.00182
22000 2464 484000000 25556351 1.48148 1319517.7 1317875 1.00125
23000 2564 529000000 27800938 1.39683 1347024.9 1344799 1.00166
24000 2668 576000000 30135807 2.66667 2775143.2 2770911 1.00153
25000 2762 625000000 32560335 1.33333 1492839.7 1490400 1.00164
26000 2860 676000000 35073432 1.45455 1747095.7 1743985 1.00178
27000 2961 729000000 37675354 2.66667 3427188.7 3420384 1.00199
28000 3055 784000000 40365081 1.60000 2194826.7 2192216 1.00119
29000 3153 841000000 43144081 1.38272 2020069.8 2016853 1.00159
30000 3245 900000000 46009215 2.66667 4140044.5 4132595 1.00180
31000 3340 961000000 48963799 1.37931 2271328.6
32000 3432 1024000000 52005085 1.33333 2324467.5
33000 3538 1089000000 55133730 2.96296 5459184.3
34000 3638 1156000000 58348154 1.42222 2764777.0
35000 3732 1225000000 61649818 1.60000 3276765.1
36000 3824 1296000000 65037966 2.66667 5745091.7
37000 3923 1369000000 68512967 1.37143 3103958.9
38000 4017 1444000000 72072759 1.41176 3352273.2
39000 4107 1521000000 75719912 2.90909 7238549.8
40000 4203 1600000000 79451833 1.33333 3472410.4
41000 4291 1681000000 83268774 1.36752 3723371.7
42000 4392 1764000000 87171749 3.20000 9099332.9
43000 4494 1849000000 91159487 1.36585 4052085.3
44000 4579 1936000000 95231759 1.48148 4581029.9
45000 4675 2025000000 99390077 2.66667 8586957.3
46000 4761 2116000000 103632567 1.39683 4679823.4
47000 4851 2209000000 107958309 1.36296 4746919.4
48000 4946 2304000000 112370370 2.66667 9647217.0
49000 5035 2401000000 116864544 1.60000 6007673.7
50000 5133 2500000000 121443371 1.33333 5192303.2
51000 5222 2601000000 126108286 2.84444 11480446.6
52000 5319 2704000000 130854465 1.45455 6080129.0
53000 5408 2809000000 135684197 1.35948 5881586.4
54000 5500 2916000000 140598249 2.66667 11933214.8
55000 5590 3025000000 145594641 1.48148 6852967.6
56000 5683 3136000000 150675094 1.60000 7646179.9
57000 5782 3249000000 155838866 2.82353 13931963.8
58000 5873 3364000000 161084762 1.38272 7040518.9
59000 5963 3481000000 166414790 1.35673 7125100.1
60000 6057 3600000000 171827136 2.66667 14436752.7
61000 6145 3721000000 177322748 1.35593 7563581.9
62000 6232 3844000000 182900591 1.37931 7923729.4
63000 6320 3969000000 188559759 3.20000 18922921.9
64000 6413 4096000000 194300622 1.33333 8112391.5
65000 6493 4225000000 200124895 1.45455 9101752.8
66000 6591 4356000000 206031571 2.96296 19060246.5
67000 6675 4489000000 212018922 1.35385 8949360.6
68000 6774 4624000000 218089695 1.42222 9657024.8
69000 6854 4761000000 224242755 2.79365 19477563.5
70000 6935 4900000000 230475545 1.60000 11449799.2
71000 7033 5041000000 236790617 1.35266 9931722.3
72000 7128 5184000000 243186912 2.66667 20082097.8
73000 7218 5329000000 249665429 1.35211 10440210.9
74000 7301 5476000000 256224887 1.37143 10853705.3
75000 7393 5625000000 262865922 2.66667 21624235.0
76000 7484 5776000000 269588250 1.41176 11726363.2
77000 7567 5929000000 276390330 1.77778 15120575.9
78000 7662 6084000000 283274401 2.90909 25328510.7
79000 7746 6241000000 290240688 1.35065 12034616.1
80000 7837 6400000000 297285198 1.33333 12154380.8
81000 7925 6561000000 304411462 2.66667 24862711.1
82000 8017 6724000000 311618852 1.36752 13037127.6
83000 8106 6889000000 318905607 1.34979 13154187.2
84000 8190 7056000000 326274451 3.20000 31870299.1
85000 8277 7225000000 333722352 1.42222 14472016.8
86000 8362 7396000000 341250966 1.36585 14196594.0
87000 8450 7569000000 348860524 2.76543 29353339.2
88000 8543 7744000000 356547745 1.48148 16054465.8
89000 8619 7921000000 364317781 1.34866 14918073.1
90000 8713 8100000000 372168766 2.66667 30101880.3
91000 8802 8281000000 380099304 1.74545 20102505.7
92000 8887 8464000000 388107832 1.39683 16409743.5
93000 8984 8649000000 396197499 2.75862 33050669.1
94000 9070 8836000000 404365549 1.36296 16649744.0
95000 9157 9025000000 412614621 1.41176 17580671.6
96000 9252 9216000000 420941249 2.66667 33845469.8
97000 9336 9409000000 429350368 1.34737 17426015.2
98000 9418 9604000000 437837670 1.60000 21082679.0
99000 9505 9801000000 446406504 2.96296 39769375.1
100000 9592 10000000000 455052511 1.33333 18226104.6 18200488 1.00141

yangchuanju · 发表于 2022-9-25 19:24

本帖最后由 yangchuanju 于 2022-9-25 22:19 编辑

x π(x) x^2 π(x^2) 波动因子白平方式计算值哥猜数真值白/哥
10000 1229 100000000 5761455 1.33333 292057.4 291400 1.00226
20000 2262 400000000 21336326 1.33333 1001558.5 999700 1.00186
30000 3245 900000000 46009215 2.66667 4140044.5 4132595 1.00180
40000 4203 1600000000 79451833 1.33333 3472410.4 3467407 1.00144
50000 5133 2500000000 121443371 1.33333 5192303.2 5185533 1.00131
60000 6057 3600000000 171827136 2.66667 14436752.7
70000 6935 4900000000 230475545 1.60000 11449799.2
80000 7837 6400000000 297285198 1.33333 12154380.8
90000 8713 8100000000 372168766 2.66667 30101880.3
100000 9592 10000000000 455052511 1.33333 18226104.6 18200488 1.00141
110000 10453 12100000000 545864306 1.48148 24083190.3
120000 11301 14400000000 644550922 2.66667 50787388.3
130000 12159 16900000000 751060249 1.45455 32049885.8
140000 13010 19600000000 865335133 1.60000 40352451.7
150000 13848 22500000000 987343369 2.66667 76271249.3
160000 14683 25600000000 1117034447 1.33333 42901342.9
170000 15497 28900000000 1254376178 1.42222 51116944.1
180000 16342 32400000000 1399331489 2.66667 106391074.1
190000 17170 36100000000 1551870851 1.41176 62173749.7
200000 17984 40000000000 1711955433 1.33333 64491864.2
210000 18807 44100000000 1879562930 3.20000 169225903.2
220000 19618 48400000000 2054662457 1.48148 85304893.3
230000 20437 52900000000 2237237738 1.39683 87247539.9
240000 21221 57600000000 2427255367 2.66667 180061140.2
250000 22044 62500000000 2624687920 1.33333 97019084.0
260000 22837 67600000000 2829520068 1.45455 113723325.0
270000 23642 72900000000 3041732620 2.66667 223422508.8
280000 24432 78400000000 3261302137 1.60000 143294619.6
290000 25224 84100000000 3488208449 1.38272 132064468.3
300000 25997 90000000000 3722428991 2.66667 271033767.1
310000 26800 96100000000 3963957671 1.37931 148881642.3
320000 27608 102400000000 4212770443 1.33333 152552411.8
330000 28404 108900000000 4468828670 2.96296 358699385.3
340000 29182 115600000000 4732159735 1.42222 181875191.0
350000 29977 122500000000 5002722471 1.60000 215795265.3
360000 30757 129600000000 5280505378 2.66667 378756461.9
370000 31522 136900000000 5565487292 1.37143 204843230.9
380000 32300 144400000000 5857663250 1.41176 221457065.3
390000 33067 152100000000 6157014054 2.90909 478645637.5
400000 33860 160000000000 6463533937 1.33333 229828917.5
410000 34614 168100000000 6777199526 1.36752 246668058.6
420000 35390 176400000000 7098011134 3.20000 603352088.4
430000 36162 184900000000 7425948444 1.36585 268916400.7
440000 36941 193600000000 7760995800 1.48148 304279040.2
450000 37706 202500000000 8103151141 2.66667 570818372.4
460000 38458 211600000000 8452398129 1.39683 311338478.5
470000 39223 220900000000 8808725055 1.36296 316053774.5
480000 40005 230400000000 9172116737 2.66667 642794300.2
490000 40766 240100000000 9542585532 1.60000 400596025.0
500000 41538 250000000000 9920079604 1.33333 346478113.6
510000 42291 260100000000 10304627621 2.84444 766599522.5
520000 43061 270400000000 10696202934 1.45455 406281252.3
530000 43825 280900000000 11094802158 1.35948 393283983.0
540000 44572 291600000000 11500409580 2.66667 798463122.4
550000 45322 302500000000 11913024161 1.48148 458840759.4
560000 46072 313600000000 12332626628 1.60000 512273926.0
570000 46819 324900000000 12759222326 2.82353 933981401.9
580000 47588 336400000000 13192789884 1.38272 472277848.2
590000 48351 348100000000 13633319902 1.35673 478231768.5
600000 49098 360000000000 14080812200 2.66667 969547333.4
610000 49861 372100000000 14535254205 1.35593 508242513.0
620000 50612 384400000000 14996633366 1.37931 532737946.3
630000 51341 396900000000 15464955307 3.20000 1272957005.0
640000 52074 409600000000 15940202960 1.33333 546026908.7
650000 52831 422500000000 16422370481 1.45455 612942706.5
660000 53564 435600000000 16911467775 2.96296 1284247137.5
670000 54309 448900000000 17407448715 1.35385 603306007.5
680000 55063 462400000000 17910338451 1.42222 651335802.3
690000 55815 476100000000 18420116956 2.79365 1314336209.3
700000 56543 490000000000 18936775942 1.60000 773007649.2
710000 57306 504100000000 19460317955 1.35266 670839605.9
720000 58029 518400000000 19990736827 2.66667 1357091788.5
730000 58789 532900000000 20528018235 1.35211 705844649.8
740000 59531 547600000000 21072156117 1.37143 734134529.1
750000 60238 562500000000 21623149145 2.66667 1463295626.1
760000 60978 577600000000 22180977051 1.41176 793861049.3
770000 61733 592900000000 22745645032 1.77778 1024095790.5
780000 62468 608400000000 23317152986 2.90909 1716197267.1
790000 63206 624100000000 23895480924 1.35065 815770669.0
800000 63951 640000000000 24480636752 1.33333 824237394.9
810000 64683 656100000000 25072614748 2.66667 1686732099.4
820000 65416 672400000000 25671393957 1.36752 884817099.1
830000 66161 688900000000 26276975917 1.34979 893121132.3
840000 66890 705600000000 26889370314 3.20000 2164715918.7
850000 67617 722500000000 27508535894 1.42222 983360653.6
860000 68342 739600000000 28134510924 1.36585 965015521.9
870000 69095 756900000000 28767273539 2.76543 1996044479.6
880000 69823 774400000000 29406803035 1.48148 1092131282.1
890000 70555 792100000000 30053094294 1.34866 1015193650.1
900000 71274 810000000000 30706162642 2.66667 2049194540.2
910000 72026 828100000000 31365996441 1.74545 1368964994.4
920000 72734 846400000000 32032574113 1.39683 1117888725.3
930000 73474 864900000000 32705908011 2.75862 2252303768.5
940000 74187 883600000000 33385994030 1.36296 1135025035.5
950000 74907 902500000000 34072815815 1.41176 1198890868.7
960000 75618 921600000000 34766377806 2.66667 2308839100.3
970000 76350 940900000000 35466674593 1.34737 1189138301.0
980000 77067 960400000000 36173704275 1.60000 1439137697.4
990000 77777 980100000000 36887443015 2.96296 2715573152.5
1000000 78498 1000000000000 37607912018 1.33333 1244932397.4 1243722370 1.00097

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特大偶数强哥猜数的估算

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