哥猜连乘积误差估计

yangchuanju · 发表于 2026-6-8 06:56

哥猜连乘积误差估计
哥猜连乘积存在较大的误差，并且随着偶数的增大，误差越来越大——
指数偶数平方根最大素数连乘积波动因子哥猜数
1 10 3 3 0.3333 1.3333 2
2 100 10 7 0.1429 1.3333 6
3 1000 32 31 0.0621 1.3333 28
4 10000 100 97 0.0383 1.3333 127
5 100000 316 313 0.0246 1.3333 810
6 1000000 1000 997 0.0173 1.3333 5402
7 10000000 3162 3137 0.0128 1.3333 38807
8 100000000 10000 9973 0.0098 1.3333 291400
9 1000000000 31623 31607 0.0077 1.3333 2274205
10 10000000000 100000 99991 0.0063 1.3333 18200488
11 1E+11 316228 316223 0.0052 1.3333 149091160
12 1E+12 1000000 999983 0.0044 1.3333 1243722370
13 1E+13 3162278 3162277 0.0037 1.3333 10533150855
14 1E+14 10000000 9999991 0.0032 1.3333 90350630388
15 1E+15 31622777 31622743 0.0028 1.3333 783538341852
16 1E+16 100000000 99999989 0.0025 1.3333 6852674128787

指数连乘哥数哈李哥数连乘/哥数哈李/哥数连乘积倒数连乘/哈李
1 1.11 1.66 0.5556 0.8301 3 0.669267491
2 4.76 4.15 0.7937 0.6917 7 1.1473157
3 20.70 18.45 0.7392 0.6588 16.10525834 1.1220076
4 127.66 103.76 1.0052 0.8170 26.11167785 1.230286302
5 820.39 664.08 1.0128 0.8198 40.63124899 1.235380726
6 5770.88 4611.64 1.0683 0.8537 57.76129626 1.251372351
7 42642.3 33881.4 1.0988 0.8731 78.16968292 1.258573881
8 326294.4 259404.7 1.1197 0.8902 102.1572306 1.257858671
9 2582599.6 2049617.1 1.1356 0.9012 129.0689193 1.260039995
10 20921398.5 16601898.7 1.1495 0.9122 159.3265062 1.260181072
11 172979150.7 137205774.6 1.1602 0.9203 192.701451 1.260727919
12 1453644840 1152909634 1.1688 0.9270 229.3086483 1.260848897
13 12386409457 9823608711 1.1759 0.9326 269.1121543 1.260881802
14 1.06805E+11 84703564910 1.1821 0.9375 312.096237 1.260922877
15 9.30385E+11 7.37862E+11 1.1874 0.9417 358.2746443 1.260919699
16 8.17732E+12 6.48512E+12 1.1933 0.9464 407.631386 1.260936844

yangchuanju · 发表于 2026-6-8 06:58

当10的幂次更高时，准确的哥猜数尚不知道；一亿内所有素数的连乘积虽可算出，更大的素数连乘积不便一一计算。
以下以万为单位，分别计算2万、3万……10万、20万……100万、200万……1000万、2000万……10000万的拟连乘积，然后用哈李对数计算式代替相应幂数的哥猜数，
再根据它们的拟连乘积、拟哥猜数，从而估算连乘积与哥猜数的比值。
由于10000万以内的具体素数不可能一一列入，取各个万间的平均奇数当成素数的平均值，素数个数用素数定理式算出；
因这些大数的连乘积是一些越来越小的纯小数，改用连乘积的倒数来表示，方便认识和读数。
按此处理，平均拟素数、拟素数个数、区间拟素数个数都不再是真正的素数、素数个数、区间素数个数，
导致连乘积也不再是实际连乘积，（连乘积倒数变小一些）拟连乘积变大，从而连乘积与哈李对数式哥猜数的比值变大一些；
在这里我们只想看比值的变化趋势，不追求比值的确切数值；随着偶数的不断增大，连乘积计算值与哈李哥猜数的比值将趋近于无穷大！

万数平方根平均拟素数拟素数个数区间个数连乘积倒数拟连乘积哈李哥猜数比值实际连乘积倒数
1 100 50 22 22 26.1117 127.66 103.74 1.2306 26.1117
2 141 121 29 7 29.2754 227.72 179.45 1.2690
3 173 157 34 5 31.2266 320.24 248.41 1.2891
4 200 187 38 4 32.6530 408.33 313.48 1.3026
5 224 212 41 4 33.7828 493.35 375.85 1.3126
6 245 234 45 3 34.7209 576.02 436.20 1.3206
7 265 255 47 3 35.5245 656.82 494.93 1.3271
8 283 274 50 3 36.2283 736.07 552.33 1.3327
9 300 291 53 2 36.8551 814.00 608.61 1.3375
10 316 308 55 2 37.4205 890.78 663.91 1.3417 40.6312
20 447 382 73 18 41.2057 1617.90 1181.30 1.3696
30 548 497 87 14 43.5233 2297.62 1659.85 1.3842
40 632 590 98 11 45.2102 2949.19 2115.51 1.3941
50 707 670 108 10 46.5423 3580.97 2555.22 1.4014
60 775 741 116 9 47.6458 4197.64 2982.80 1.4073
70 837 806 124 8 48.5893 4802.15 3400.68 1.4121
80 894 866 132 7 49.4144 5396.54 3810.50 1.4162
90 949 922 138 7 50.1481 5982.28 4213.48 1.4198
100 1000 974 145 6 50.8092 6560.50 4610.51 1.4229 57.7613
200 1414 1207 195 50 55.2181 12073.33 8361.00 1.4440
300 1732 1573 232 37 57.9031 17270.23 11868.85 1.4551
400 2000 1866 263 31 59.8512 22277.48 15231.84 1.4626
500 2236 2118 290 27 61.3860 27150.61 18492.91 1.4682
600 2449 2343 314 24 62.6552 31920.74 21676.04 1.4726
700 2646 2548 336 22 63.7388 36607.72 24796.48 1.4763
800 2828 2737 356 20 64.6853 41225.24 27864.69 1.4795
900 3000 2914 375 19 65.5261 45783.27 30888.31 1.4822
1000 3162 3081 392 18 66.2830 50289.43 33873.12 1.4846 78.1697
2000 4472 3817 532 140 71.3161 93480.51 62274.90 1.5011
3000 5477 4975 636 104 74.3686 134465.33 89064.31 1.5098
4000 6325 5901 723 86 76.5778 174114.75 114881.13 1.5156
5000 7071 6698 798 75 78.3154 212814.77 140009.03 1.5200
6000 7746 7409 865 67 79.7502 250782.95 164607.56 1.5235
7000 8367 8056 926 61 80.9740 288158.41 188778.52 1.5264
8000 8944 8655 983 57 82.0418 325037.50 212592.25 1.5289
9000 9487 9216 1036 53 82.9897 361490.71 236100.09 1.5311
10000 10000 9743 1086 50 83.8423 397571.72 259341.08 1.5330 102.1572
20000 14142 12071 1480 394 89.4993 744884.89 481745.12 1.5462
30000 17321 15731 1775 295 92.9190 1076205.86 692908.29 1.5532
40000 20000 18660 2019 245 95.3892 1397781.80 897235.30 1.5579
50000 22361 21180 2233 213 97.3293 1712399.92 1096694.42 1.5614
60000 24495 23428 2424 191 98.9297 2021637.76 1292398.44 1.5643
70000 26458 25476 2598 174 100.2934 2326507.32 1485060.11 1.5666
80000 28284 27371 2759 161 101.4825 2627711.10 1675173.35 1.5686
90000 30000 29142 2910 151 102.5373 2925764.09 1863099.72 1.5704
100000 31623 30811 3052 142 103.4856 3221059.35 2049114.73 1.5719 129.0689
200000 44721 38172 4176 1124 109.7658 6073536.09 3837242.10 1.5828
300000 54772 49747 5020 844 113.5524 8806504.67 5543954.73 1.5885
400000 63246 59009 5721 701 116.2833 11466245.77 7200828.31 1.5924
500000 70711 66978 6332 611 118.4257 14073518.78 8822061.21 1.5953
600000 77460 74085 6881 548 120.1915 16640113.79 10415713.94 1.5976
700000 83666 80563 7381 501 121.6950 19173613.82 11986965.19 1.5995
800000 89443 86554 7845 463 123.0052 21679293.49 13539412.84 1.6012
900000 94868 92156 8278 433 124.1669 24161026.37 15075695.96 1.6026
1000000 100000 97434 8686 408 125.2108 26621773.03 16597829.34 1.6039 159.3265
2000000 141421 120711 11925 3239 132.1136 50461629.88 31283835.01 1.6130
3000000 173205 157313 14359 2435 136.2667 73385504.96 45361625.54 1.6178
4000000 200000 186603 16385 2026 139.2580 95745518.61 59065076.58 1.6210
5000000 223607 211803 18153 1768 141.6026 117700322.1 72499891.93 1.6235
6000000 244949 234278 19740 1587 143.5335 139340280.4 85726283.79 1.6254
7000000 264575 254762 21190 1450 145.1767 160723638.7 98783036.07 1.6270
8000000 282843 273709 22533 1343 146.6080 181890981.8 111697149.2 1.6284
9000000 300000 291421 23788 1255 147.8764 202872157.0 124488462.0 1.6296
10000000 316228 308114 24970 1182 149.0157 223690005.2 137172143.3 1.6307 192.7015
20000000 447214 381721 34373 9402 156.5405 425874768.2 259923313.7 1.6385
30000000 547723 497468 41452 7079 161.0598 620887345.5 378012890.3 1.6425
40000000 632456 590089 47349 5897 164.3114 811467501.2 493220447.1 1.6452
50000000 707107 669781 52499 5150 166.8578 998854326.5 606353717.0 1.6473
60000000 774597 740852 57123 4624 168.9538 1183755313.3 717874110.3 1.6490
70000000 836660 805628 61351 4228 170.7366 1366627318.3 828079465.9 1.6504
80000000 894427 865544 65268 3916 172.2888 1547789142.0 937177488.4 1.6515
90000000 948683 921555 68931 3663 173.6638 1727475529.7 1045321012.4 1.6526
100000000 1000000 974342 72382 3452 174.8986 1905866310.9 1152627037.3 1.6535 229.3086
200000000 1414214 1207107 99859 27477 183.0449 3642094293.0 2193806583.2 1.6602
300000000 1732051 1573132 120576 20717 187.9300 5321130194.9 3198480874.5 1.6636
400000000 2000000 1866025 137849 17273 191.4415 6964702088.2 4180499738.9 1.6660
500000000 2236068 2118034 152943 15095 194.1898 8582668497.4 5146172081.2 1.6678
600000000 2449490 2342779 166503 13560 196.4507 10180670239.5 6099110424.1 1.6692
700000000 2645751 2547621 178906 12403 198.3730 11762355564.4 7041650860.3 1.6704
800000000 2828427 2737089 190399 11493 200.0459 13330273491.5 7975424894.3 1.6714
900000000 3000000 2914214 201152 10752 201.5275 14886302952.8 8901634499.6 1.6723
1000000000 3162278 3081139 211286 10134 202.8576 16431884635.1 9821200791.1 1.6731 269.1122
2000000000 4472136 3817207 292041 80755 211.6249 31502274402.9 18763365769.5 1.6789
3000000000 5477226 4974681 353003 60961 216.8757 46109370365.3 27414370503.2 1.6819
4000000000 6324555 5900890 403868 50866 220.6470 60428344244.2 35884088093.5 1.6840
5000000000 7071068 6697812 448344 44476 223.5969 74538897410.0 44222721881.8 1.6855
6000000000 7745967 7408517 488314 39970 226.0226 88486716187.1 52459077509.1 1.6868
7000000000 8366600 8056283 524889 36575 228.0842 102301389065 60611811499.4 1.6878
8000000000 8944272 8655436 558789 33900 229.8779 116003612164 68693969717.8 1.6887
9000000000 9486833 9215552 590513 31724 231.4660 129608655044 76715173511.5 1.6895
10000000000 10000000 9743416 620421 29908 232.8914 143128235043 84682802739.9 1.6902 312.0962
20000000000 14142136 12071068 858938 238518 242.2793 275164542808 162310514836 1.6953
30000000000 17320508 15731322 1039185 180246 247.8954 403396022890 237579041399 1.6979
40000000000 20000000 18660254 1189680 150495 251.9263 529255229494 311374490089 1.6997
50000000000 22360680 21180340 1321333 131653 255.0778 653395548683 384102816559 1.7011
60000000000 24494897 23427789 1439693 118359 257.6682 776192110287 455997362677 1.7022
70000000000 26457513 25476205 1548033 108340 259.8690 897888156260 527209460137 1.7031
80000000000 28284271 27370892 1648477 100444 261.7834 1018653989952 597845045053 1.7039
90000000000 30000000 29142136 1742493 94016 263.4779 1138615362385 667982316815 1.7046
100000000000 31622777 30811388 1831146 88653 264.9985 1257868837632 737681303868 1.7052 358.2746
200000000000 44721360 38172068 2538684 707538 275.0066 2424184327409 1417881569623 1.7097
300000000000 54772256 49746808 3073865 535181 280.9878 3558873387881 2078701738842 1.7121
400000000000 63245553 59008904 3520970 447106 285.2783 4673799176292 2727390975395 1.7137
500000000000 70710678 66978116 3912264 391294 288.6311 5774384064581 3367278053175 1.7149
600000000000 77459667 74085173 4264163 351899 291.3861 6863745583032 4000279303818 1.7158
700000000000 83666003 80562835 4586363 322200 293.7262 7943907341433 4627639009574 1.7166
800000000000 89442719 86554361 4885149 298786 295.7611 9016287356640 5250229029704 1.7173
900000000000 94868330 92155524 5164870 279721 297.5620 10081933431761 5868693463718 1.7179
1000000000000 100000000 97434165 5428681 263811 299.1777 11141650668568 6483527084774 1.7185 407.6314

yangchuanju · 发表于 2026-6-8 07:04

万数平方根平均拟素数拟素数个数区间个数连乘积倒数拟连乘积哈李哥猜数比值
1E+12 1.000E+08 9.743E+07 5.429E+06 2.638E+05 299.1777 1.114E+13 6.484E+12 1.7185
2E+12 1.414E+08 1.207E+08 7.536E+06 2.107E+06 309.8057 2.152E+13 1.249E+13 1.7225
3E+12 1.732E+08 1.573E+08 9.130E+06 1.595E+06 316.1518 3.163E+13 1.834E+13 1.7246
4E+12 2.000E+08 1.866E+08 1.046E+07 1.333E+06 320.7016 4.158E+13 2.409E+13 1.7260
5E+12 2.236E+08 2.118E+08 1.163E+07 1.167E+06 324.2557 5.140E+13 2.976E+13 1.7271
6E+12 2.449E+08 2.343E+08 1.268E+07 1.050E+06 327.1752 6.113E+13 3.538E+13 1.7280
7E+12 2.646E+08 2.548E+08 1.364E+07 9.616E+05 329.6544 7.078E+13 4.095E+13 1.7287
8E+12 2.828E+08 2.737E+08 1.453E+07 8.919E+05 331.8098 8.037E+13 4.647E+13 1.7293
9E+12 3.000E+08 2.914E+08 1.537E+07 8.351E+05 333.7171 8.990E+13 5.197E+13 1.7298
1E+13 3.162E+08 3.081E+08 1.616E+07 7.878E+05 335.4279 9.938E+13 5.743E+13 1.7303
2E+13 4.472E+08 3.817E+08 2.245E+07 6.295E+06 346.6754 1.923E+14 1.109E+14 1.7340
3E+13 5.477E+08 4.975E+08 2.722E+07 4.769E+06 353.3863 2.830E+14 1.630E+14 1.7359
4E+13 6.325E+08 5.901E+08 3.121E+07 3.988E+06 358.1953 3.722E+14 2.143E+14 1.7371
5E+13 7.071E+08 6.698E+08 3.470E+07 3.493E+06 361.9506 4.605E+14 2.649E+14 1.7381
6E+13 7.746E+08 7.409E+08 3.784E+07 3.143E+06 365.0346 5.479E+14 3.151E+14 1.7389
7E+13 8.367E+08 8.056E+08 4.072E+07 2.879E+06 367.6528 6.347E+14 3.648E+14 1.7395
8E+13 8.944E+08 8.655E+08 4.339E+07 2.671E+06 369.9287 7.209E+14 4.143E+14 1.7401
9E+13 9.487E+08 9.216E+08 4.590E+07 2.501E+06 371.9421 8.066E+14 4.634E+14 1.7405
1E+14 1.000E+09 9.743E+08 4.825E+07 2.360E+06 373.7480 8.919E+14 5.123E+14 1.7410
2E+14 1.414E+09 1.207E+09 6.712E+07 1.887E+07 385.6148 1.729E+15 9.911E+14 1.7443
3E+14 1.732E+09 1.573E+09 8.142E+07 1.430E+07 392.6903 2.547E+15 1.458E+15 1.7460
4E+14 2.000E+09 1.866E+09 9.339E+07 1.196E+07 397.7584 3.352E+15 1.919E+15 1.7472
5E+14 2.236E+09 2.118E+09 1.039E+08 1.048E+07 401.7147 4.149E+15 2.373E+15 1.7480
6E+14 2.449E+09 2.343E+09 1.133E+08 9.434E+06 404.9630 4.939E+15 2.824E+15 1.7487
7E+14 2.646E+09 2.548E+09 1.219E+08 8.643E+06 407.7203 5.723E+15 3.272E+15 1.7493
8E+14 2.828E+09 2.737E+09 1.300E+08 8.020E+06 410.1165 6.502E+15 3.716E+15 1.7498
9E+14 3.000E+09 2.914E+09 1.375E+08 7.512E+06 412.2362 7.277E+15 4.158E+15 1.7502
1E+15 3.162E+09 3.081E+09 1.446E+08 7.087E+06 414.1371 8.049E+15 4.598E+15 1.7506
2E+15 4.472E+09 3.817E+09 2.013E+08 5.669E+07 426.6229 1.563E+16 8.911E+15 1.7537
3E+15 5.477E+09 4.975E+09 2.443E+08 4.300E+07 434.0627 2.304E+16 1.313E+16 1.7552
4E+15 6.325E+09 5.901E+09 2.802E+08 3.599E+07 439.3898 3.035E+16 1.728E+16 1.7562
5E+15 7.071E+09 6.698E+09 3.118E+08 3.154E+07 443.5472 3.758E+16 2.139E+16 1.7570
6E+15 7.746E+09 7.409E+09 3.402E+08 2.839E+07 446.9598 4.475E+16 2.546E+16 1.7576
7E+15 8.367E+09 8.056E+09 3.662E+08 2.602E+07 449.8559 5.187E+16 2.950E+16 1.7582
8E+15 8.944E+09 8.655E+09 3.903E+08 2.414E+07 452.3725 5.895E+16 3.352E+16 1.7586
9E+15 9.487E+09 9.216E+09 4.130E+08 2.262E+07 454.5984 6.599E+16 3.752E+16 1.7590
1E+16 1.000E+10 9.743E+09 4.343E+08 2.134E+07 456.5943 7.300E+16 4.149E+16 1.7594
2E+16 1.414E+10 1.207E+10 6.051E+08 1.708E+08 469.6987 1.419E+17 8.055E+16 1.7622
3E+16 1.732E+10 1.573E+10 7.347E+08 1.296E+08 477.5028 2.094E+17 1.188E+17 1.7636
4E+16 2.000E+10 1.866E+10 8.432E+08 1.085E+08 483.0888 2.760E+17 1.564E+17 1.7645
5E+16 2.236E+10 2.118E+10 9.383E+08 9.511E+07 487.4471 3.419E+17 1.937E+17 1.7652
6E+16 2.449E+10 2.343E+10 1.024E+09 8.564E+07 491.0239 4.073E+17 2.307E+17 1.7658
7E+16 2.646E+10 2.548E+10 1.102E+09 7.849E+07 494.0589 4.723E+17 2.674E+17 1.7663
8E+16 2.828E+10 2.737E+10 1.175E+09 7.285E+07 496.6958 5.369E+17 3.039E+17 1.7667
9E+16 3.000E+10 2.914E+10 1.244E+09 6.825E+07 499.0278 6.012E+17 3.402E+17 1.7670
1E+17 3.162E+10 3.081E+10 1.308E+09 6.441E+07 501.1186 6.652E+17 3.764E+17 1.7674
2E+17 4.472E+10 3.817E+10 1.824E+09 5.156E+08 514.8415 1.295E+18 7.316E+17 1.7699
3E+17 5.477E+10 4.975E+10 2.215E+09 3.915E+08 523.0097 1.912E+18 1.079E+18 1.7712
4E+17 6.325E+10 5.901E+10 2.543E+09 3.279E+08 528.8544 2.521E+18 1.423E+18 1.7721
5E+17 7.071E+10 6.698E+10 2.830E+09 2.875E+08 533.4136 3.125E+18 1.763E+18 1.7727
6E+17 7.746E+10 7.409E+10 3.089E+09 2.589E+08 537.1545 3.723E+18 2.100E+18 1.7733
7E+17 8.367E+10 8.056E+10 3.327E+09 2.373E+08 540.3283 4.318E+18 2.435E+18 1.7737
8E+17 8.944E+10 8.655E+10 3.547E+09 2.203E+08 543.0855 4.910E+18 2.768E+18 1.7741
9E+17 9.487E+10 9.216E+10 3.753E+09 2.064E+08 545.5236 5.499E+18 3.099E+18 1.7744
1E+18 1.000E+11 9.743E+10 3.948E+09 1.948E+08 547.7092 6.086E+18 3.429E+18 1.7747
2E+18 1.414E+11 1.207E+11 5.508E+09 1.560E+09 562.0504 1.186E+19 6.675E+18 1.7771
3E+18 1.732E+11 1.573E+11 6.693E+09 1.185E+09 570.5825 1.753E+19 9.856E+18 1.7782
4E+18 2.000E+11 1.866E+11 7.686E+09 9.927E+08 576.6858 2.312E+19 1.300E+19 1.7790
5E+18 2.236E+11 2.118E+11 8.556E+09 8.705E+08 581.4457 2.866E+19 1.611E+19 1.7796
6E+18 2.449E+11 2.343E+11 9.341E+09 7.841E+08 585.3508 3.417E+19 1.919E+19 1.7801
7E+18 2.646E+11 2.548E+11 1.006E+10 7.188E+08 588.6633 3.964E+19 2.226E+19 1.7805
8E+18 2.828E+11 2.737E+11 1.073E+10 6.673E+08 591.5407 4.508E+19 2.531E+19 1.7809
9E+18 3.000E+11 2.914E+11 1.135E+10 6.253E+08 594.0848 5.050E+19 2.835E+19 1.7812
1E+19 3.162E+11 3.081E+11 1.194E+10 5.903E+08 596.3654 5.589E+19 3.138E+19 1.7814
2E+19 4.472E+11 3.817E+11 1.667E+10 4.728E+09 611.3243 1.091E+20 6.114E+19 1.7836
3E+19 5.477E+11 4.975E+11 2.026E+10 3.594E+09 620.2203 1.612E+20 9.034E+19 1.7847
4E+19 6.325E+11 5.901E+11 2.328E+10 3.011E+09 626.5822 2.128E+20 1.192E+20 1.7855
5E+19 7.071E+11 6.698E+11 2.592E+10 2.641E+09 631.5428 2.639E+20 1.478E+20 1.7860
6E+19 7.746E+11 7.409E+11 2.830E+10 2.379E+09 635.6119 3.147E+20 1.761E+20 1.7865
7E+19 8.367E+11 8.056E+11 3.048E+10 2.181E+09 639.0631 3.651E+20 2.043E+20 1.7868
8E+19 8.944E+11 8.655E+11 3.250E+10 2.025E+09 642.0605 4.153E+20 2.324E+20 1.7871
9E+19 9.487E+11 9.216E+11 3.440E+10 1.898E+09 644.7107 4.653E+20 2.603E+20 1.7874
1E+20 1.000E+12 9.743E+11 3.619E+10 1.792E+09 647.0859 5.151E+20 2.882E+20 1.7877
2E+20 1.414E+12 1.207E+12 5.055E+10 1.436E+10 662.6632 1.006E+21 5.621E+20 1.7897
3E+20 1.732E+12 1.573E+12 6.146E+10 1.092E+10 671.9236 1.488E+21 8.311E+20 1.7907
4E+20 2.000E+12 1.866E+12 7.061E+10 9.148E+09 678.5441 1.965E+21 1.097E+21 1.7914
5E+20 2.236E+12 2.118E+12 7.864E+10 8.025E+09 683.7058 2.438E+21 1.360E+21 1.7919
6E+20 2.449E+12 2.343E+12 8.587E+10 7.230E+09 687.9392 2.907E+21 1.622E+21 1.7923
7E+20 2.646E+12 2.548E+12 9.250E+10 6.630E+09 691.5297 3.374E+21 1.882E+21 1.7927
8E+20 2.828E+12 2.737E+12 9.865E+10 6.156E+09 694.6476 3.839E+21 2.141E+21 1.7930
9E+20 3.000E+12 2.914E+12 1.044E+11 5.770E+09 697.4038 4.302E+21 2.399E+21 1.7932
1E+21 3.162E+12 3.081E+12 1.099E+11 5.447E+09 699.8737 4.763E+21 2.656E+21 1.7934
2E+21 4.472E+12 3.817E+12 1.535E+11 4.366E+10 716.0708 9.310E+21 5.186E+21 1.7953
3E+21 5.477E+12 4.975E+12 1.867E+11 3.321E+10 725.6964 1.378E+22 7.671E+21 1.7963
4E+21 6.325E+12 5.901E+12 2.146E+11 2.784E+10 732.5734 1.820E+22 1.013E+22 1.7969
5E+21 7.071E+12 6.698E+12 2.390E+11 2.442E+10 737.9360 2.259E+22 1.257E+22 1.7974
6E+21 7.746E+12 7.409E+12 2.610E+11 2.201E+10 742.3338 2.694E+22 1.499E+22 1.7978
7E+21 8.367E+12 8.056E+12 2.812E+11 2.018E+10 746.0623 3.128E+22 1.739E+22 1.7981
8E+21 8.944E+12 8.655E+12 2.999E+11 1.874E+10 749.3012 3.559E+22 1.979E+22 1.7983
9E+21 9.487E+12 9.216E+12 3.175E+11 1.757E+10 752.1621 3.989E+22 2.218E+22 1.7986
1E+22 1.000E+13 9.743E+12 3.341E+11 1.658E+10 754.7258 4.417E+22 2.455E+22 1.7988
2E+22 1.414E+13 1.207E+13 4.670E+11 1.330E+11 771.5337 8.641E+22 4.799E+22 1.8006
3E+22 1.732E+13 1.573E+13 5.682E+11 1.012E+11 781.5283 1.280E+23 7.103E+22 1.8015
4E+22 2.000E+13 1.866E+13 6.530E+11 8.482E+10 788.6700 1.691E+23 9.382E+22 1.8020
5E+22 2.236E+13 2.118E+13 7.275E+11 7.443E+10 794.2290 2.098E+23 1.164E+23 1.8025
6E+22 2.449E+13 2.343E+13 7.945E+11 6.708E+10 798.7844 2.504E+23 1.389E+23 1.8028
7E+22 2.646E+13 2.548E+13 8.560E+11 6.152E+10 802.6564 2.907E+23 1.612E+23 1.8031
8E+22 2.828E+13 2.737E+13 9.132E+11 5.713E+10 806.0135 3.308E+23 1.835E+23 1.8034
9E+22 3.000E+13 2.914E+13 9.667E+11 5.356E+10 808.9807 3.708E+23 2.056E+23 1.8036
1E+23 3.162E+13 3.081E+13 1.017E+12 5.057E+10 811.6373 4.107E+23 2.277E+23 1.8038
2E+23 4.472E+13 3.817E+13 1.423E+12 4.055E+11 829.0693 8.041E+23 4.454E+23 1.8055
3E+23 5.477E+13 4.975E+13 1.731E+12 3.086E+11 839.4161 1.191E+24 6.595E+23 1.8063
4E+23 6.325E+13 5.901E+13 1.990E+12 2.588E+11 846.8290 1.575E+24 8.714E+23 1.8068
5E+23 7.071E+13 6.698E+13 2.217E+12 2.271E+11 852.5713 1.955E+24 1.082E+24 1.8073
6E+23 7.746E+13 7.409E+13 2.422E+12 2.047E+11 857.3124 2.333E+24 1.291E+24 1.8076
7E+23 8.367E+13 8.056E+13 2.610E+12 1.878E+11 861.3252 2.709E+24 1.498E+24 1.8078
8E+23 8.944E+13 8.655E+13 2.784E+12 1.744E+11 864.8010 3.084E+24 1.705E+24 1.8081
9E+23 9.487E+13 9.216E+13 2.948E+12 1.635E+11 867.8831 3.457E+24 1.912E+24 1.8083
1E+24 1.000E+14 9.743E+13 3.102E+12 1.544E+11 870.6243 3.829E+24 2.117E+24 1.8085

yangchuanju · 发表于 2026-6-8 07:06

简表——仅取10的幂数，由于其间跨度变得更大，导致拟连乘积与哈李哥猜数的比值更大一些，但总的变化趋势不变——
万数平方根平均拟素数拟素数个数区间个数连乘积倒数拟连乘积哈李哥猜数比值
1 100 50 22 22 26.1117 127.66 103.74 1.2306
10 316 208 55 33 35.9875 926.25 663.91 1.3951
100 1000 658 145 90 47.3033 7046.72 4610.51 1.5284
1000 3162 2081 392 248 60.0192 55537.78 33873.12 1.6396
10000 10000 6581 1086 693 74.0992 449847.65 259341.08 1.7346
100000 31623 20811 3052 1966 89.5113 3723923.96 2049114.73 1.8173
1000000 100000 65811 8686 5634 106.2276 31379176.33 16597829.34 1.8906
10000000 316228 208114 24970 16284 124.2230 268334633.9 137172143.3 1.9562
100000000 1000000 658114 72382 47412 143.4754 2323278249.0 1152627037.3 2.0156
1000000000 3162278 2081139 211286 138904 163.9648 20329562191 9821200791 2.0700
10000000000 10000000 6581139 620421 409135 185.6731 179527010341 84682802740 2.1200
1E+11 3.162E+07 2.081E+07 1.831E+06 1.211E+06 208.5836 1.598E+12 7.377E+11 2.1664
1E+12 1.000E+08 6.581E+07 5.429E+06 3.598E+06 232.6810 1.433E+13 6.484E+12 2.2096
1E+13 3.162E+08 2.081E+08 1.616E+07 1.073E+07 257.9512 1.292E+14 5.743E+13 2.2500
1E+14 1.000E+09 6.581E+08 4.825E+07 3.210E+07 284.3811 1.172E+15 5.123E+14 2.2881
1E+15 3.162E+09 2.081E+09 1.446E+08 9.631E+07 311.9583 1.069E+16 4.598E+15 2.3240
1E+16 1.000E+10 6.581E+09 4.343E+08 2.897E+08 340.6714 9.785E+16 4.149E+16 2.3580
1E+17 3.162E+10 2.081E+10 1.308E+09 8.737E+08 370.5093 8.997E+17 3.764E+17 2.3904
1E+18 1.000E+11 6.581E+10 3.948E+09 2.640E+09 401.4621 8.303E+18 3.429E+18 2.4212
1E+19 3.162E+11 2.081E+11 1.194E+10 7.994E+09 433.5198 7.689E+19 3.138E+19 2.4506
1E+20 1.000E+12 6.581E+11 3.619E+10 2.425E+10 466.6725 7.143E+20 2.882E+20 2.4788
1E+21 3.162E+12 2.081E+12 1.099E+11 7.368E+10 500.9130 6.655E+21 2.656E+21 2.5058
1E+22 1.000E+13 6.581E+12 3.341E+11 2.242E+11 536.2421 6.216E+22 2.455E+22 2.5317
1E+23 3.162E+13 2.081E+13 1.017E+12 6.832E+11 572.6503 5.821E+23 2.277E+23 2.5566
1E+24 1.000E+14 6.581E+13 3.102E+12 2.085E+12 610.1440 5.463E+24 2.117E+24 2.5805
1E+25 3.162E+14 2.081E+14 9.471E+12 6.369E+12 648.4008 5.141E+25 1.974E+25 2.6048
1E+26 1.000E+15 6.581E+14 2.895E+13 1.948E+13 688.8818 4.839E+26 1.844E+26 2.6238
1E+27 3.162E+15 2.081E+15 8.860E+13 5.965E+13 726.3634 4.589E+27 1.727E+27 2.6570
1E+28 1.000E+16 6.581E+15 2.714E+14 1.828E+14 756.4579 4.407E+28 1.621E+28 2.7186
1E+29 3.162E+16 2.081E+16 8.323E+14 5.609E+14 756.4579 4.407E+29 1.524E+29 2.8911
1E+30 1.000E+17 6.581E+16 2.555E+15 1.722E+15 756.4579 4.407E+30 1.436E+30 3.0690
1E+31 3.162E+17 2.081E+17 7.848E+15 5.293E+15 756.4579 4.407E+31 1.355E+31 3.2522
1E+32 1.000E+18 6.581E+17 2.413E+16 1.628E+16 756.4579 4.407E+32 1.281E+32 3.4407
1E+33 3.162E+18 2.081E+18 7.424E+16 5.011E+16 756.4579 4.407E+33 1.212E+33 3.6345
1E+34 1.000E+19 6.581E+18 2.286E+17 1.543E+17 756.4579 4.407E+34 1.149E+34 3.8336
1E+35 3.162E+19 2.081E+19 7.043E+17 4.757E+17 756.4579 4.407E+35 1.091E+35 4.0381
1E+36 1.000E+20 6.581E+19 2.171E+18 1.467E+18 756.4579 4.407E+36 1.037E+36 4.2478
1E+37 3.162E+20 2.081E+20 6.699E+18 4.528E+18 756.4579 4.407E+37 9.874E+36 4.4628
1E+38 1.000E+21 6.581E+20 2.068E+19 1.398E+19 756.4579 4.407E+38 9.409E+37 4.6832
1E+39 3.162E+21 2.081E+21 6.388E+19 4.320E+19 756.4579 4.407E+39 8.977E+38 4.9088
1E+40 1.000E+22 6.581E+21 1.974E+20 1.335E+20 756.4579 4.407E+40 8.573E+39 5.1398
1E+41 3.162E+22 2.081E+22 6.104E+20 4.130E+20 756.4579 4.407E+41 8.196E+40 5.3761
1E+42 1.000E+23 6.581E+22 1.888E+21 1.278E+21 756.4579 4.407E+42 7.844E+41 5.6177
1E+43 3.162E+23 2.081E+23 5.844E+21 3.956E+21 756.4579 4.407E+43 7.514E+42 5.8646
1E+44 1.000E+24 6.581E+23 1.810E+22 1.225E+22 756.4579 4.407E+44 7.204E+43 6.1168
1E+45 3.162E+24 2.081E+24 5.606E+22 3.796E+22 756.4579 4.407E+45 6.913E+44 6.3743
1E+46 1.000E+25 6.581E+24 1.737E+23 1.177E+23 756.4579 4.407E+46 6.639E+45 6.6372
1E+47 3.162E+25 2.081E+25 5.386E+23 3.649E+23 756.4579 4.407E+47 6.381E+46 6.9053
1E+48 1.000E+26 6.581E+25 1.670E+24 1.132E+24 756.4579 4.407E+48 6.138E+47 7.1788
1E+49 3.162E+26 2.081E+26 5.182E+24 3.512E+24 756.4579 4.407E+49 5.909E+48 7.4575
1E+50 1.000E+27 6.581E+26 1.608E+25 1.090E+25 756.4579 4.407E+50 5.692E+49 7.7416
1E+51 3.162E+27 2.081E+27 4.994E+25 3.386E+25 756.4579 4.407E+51 5.487E+50 8.0310
1E+52 1.000E+28 6.581E+27 1.551E+26 1.052E+26 756.4579 4.407E+52 5.293E+51 8.3257
1E+53 3.162E+28 2.081E+28 4.819E+26 3.268E+26 756.4579 4.407E+53 5.109E+52 8.6257
1E+54 1.000E+29 6.581E+28 1.498E+27 1.016E+27 756.4579 4.407E+54 4.934E+53 8.9310
1E+55 3.162E+29 2.081E+29 4.655E+27 3.158E+27 756.4579 4.407E+55 4.768E+54 9.2416
1E+56 1.000E+30 6.581E+29 1.448E+28 9.821E+27 756.4579 4.407E+56 4.611E+55 9.5575
1E+57 3.162E+30 2.081E+30 4.503E+28 3.055E+28 756.4579 4.407E+57 4.461E+56 9.8788
1E+58 1.000E+31 6.581E+30 1.401E+29 9.507E+28 756.4579 4.407E+58 4.318E+57 10.2053
1E+59 3.162E+31 2.081E+31 4.360E+29 2.959E+29 756.4579 4.407E+59 4.182E+58 10.5372
1E+60 1.000E+32 6.581E+31 1.357E+30 9.212E+29 756.4579 4.407E+60 4.052E+59 10.8743
1E+61 3.162E+32 2.081E+32 4.226E+30 2.869E+30 756.4579 4.407E+61 3.928E+60 11.2168
1E+62 1.000E+33 6.581E+32 1.316E+31 8.935E+30 756.4579 4.407E+62 3.810E+61 11.5646
1E+63 3.162E+33 2.081E+33 4.100E+31 2.784E+31 756.4579 4.407E+63 3.697E+62 11.9177
1E+64 1.000E+34 6.581E+33 1.277E+32 8.674E+31 756.4579 4.407E+64 3.589E+63 12.2761
1E+65 3.162E+34 2.081E+34 3.981E+32 2.703E+32 756.4579 4.407E+65 3.486E+64 12.6398
1E+66 1.000E+35 6.581E+34 1.241E+33 8.428E+32 756.4579 4.407E+66 3.387E+65 13.0088
1E+67 3.162E+35 2.081E+35 3.869E+33 2.628E+33 756.4579 4.407E+67 3.293E+66 13.3832
1E+68 1.000E+36 6.581E+35 1.206E+34 8.195E+33 756.4579 4.407E+68 3.202E+67 13.7628
1E+69 3.162E+36 2.081E+36 3.763E+34 2.556E+34 756.4579 4.407E+69 3.115E+68 14.1478
1E+70 1.000E+37 6.581E+36 1.174E+35 7.975E+34 756.4579 4.407E+70 3.031E+69 14.5380
1E+71 3.162E+37 2.081E+37 3.662E+35 2.489E+35 756.4579 4.407E+71 2.951E+70 14.9336
1E+72 1.000E+38 6.581E+37 1.143E+36 7.767E+35 756.4579 4.407E+72 2.874E+71 15.3345
1E+73 3.162E+38 2.081E+38 3.567E+36 2.424E+36 756.4579 4.407E+73 2.799E+72 15.7407
1E+74 1.000E+39 6.581E+38 1.114E+37 7.569E+36 756.4579 4.407E+74 2.728E+73 16.1522
1E+75 3.162E+39 2.081E+39 3.477E+37 2.363E+37 756.4579 4.407E+75 2.659E+74 16.5690
1E+76 1.000E+40 6.581E+39 1.086E+38 7.381E+37 756.4579 4.407E+76 2.593E+75 16.9911
1E+77 3.162E+40 2.081E+40 3.391E+38 2.305E+38 756.4579 4.407E+77 2.530E+76 17.4186
1E+78 1.000E+41 6.581E+40 1.059E+39 7.202E+38 756.4579 4.407E+78 2.468E+77 17.8513
1E+79 3.162E+41 2.081E+41 3.309E+39 2.250E+39 756.4579 4.407E+79 2.409E+78 18.2894
1E+80 1.000E+42 6.581E+41 1.034E+40 7.031E+39 756.4579 4.407E+80 2.352E+79 18.7327
1E+81 3.162E+42 2.081E+42 3.231E+40 2.197E+40 756.4579 4.407E+81 2.297E+80 19.1814
1E+82 1.000E+43 6.581E+42 1.010E+41 6.868E+40 756.4579 4.407E+82 2.244E+81 19.6354
1E+83 3.162E+43 2.081E+43 3.157E+41 2.147E+41 756.4579 4.407E+83 2.193E+82 20.0947
1E+84 1.000E+44 6.581E+43 9.870E+41 6.713E+41 756.4579 4.407E+84 2.143E+83 20.5593
1E+85 3.162E+44 2.081E+44 3.086E+42 2.099E+42 756.4579 4.407E+85 2.095E+84 21.0292
1E+86 1.000E+45 6.581E+44 9.651E+42 6.565E+42 756.4579 4.407E+86 2.049E+85 21.5044
1E+87 3.162E+45 2.081E+45 3.018E+43 2.053E+43 756.4579 4.407E+87 2.004E+86 21.9850
1E+88 1.000E+46 6.581E+45 9.441E+43 6.423E+43 756.4579 4.407E+88 1.961E+87 22.4708
1E+89 3.162E+46 2.081E+46 2.953E+44 2.009E+44 756.4579 4.407E+89 1.919E+88 22.9619
1E+90 1.000E+47 6.581E+46 9.240E+44 6.287E+44 756.4579 4.407E+90 1.878E+89 23.4584
1E+91 3.162E+47 2.081E+47 2.891E+45 1.967E+45 756.4579 4.407E+91 1.839E+90 23.9602
1E+92 1.000E+48 6.581E+47 9.048E+45 6.157E+45 756.4579 4.407E+92 1.801E+91 24.4673
1E+93 3.162E+48 2.081E+48 2.832E+46 1.927E+46 756.4579 4.407E+93 1.764E+92 24.9796
1E+94 1.000E+49 6.581E+48 8.863E+46 6.031E+46 756.4579 4.407E+94 1.728E+93 25.4973
1E+95 3.162E+49 2.081E+49 2.774E+47 1.888E+47 756.4579 4.407E+95 1.693E+94 26.0203
1E+96 1.000E+50 6.581E+49 8.686E+47 5.911E+47 756.4579 4.407E+96 1.660E+95 26.5487
1E+97 3.162E+50 2.081E+50 2.720E+48 1.851E+48 756.4579 4.407E+97 1.627E+96 27.0823
1E+98 1.000E+51 6.581E+50 8.516E+48 5.796E+48 756.4579 4.407E+98 1.595E+97 27.6212
1E+99 3.162E+51 2.081E+51 2.667E+49 1.815E+49 756.4579 4.407E+99 1.565E+98 28.1655
1E+100 1.000E+52 6.581E+51 8.352E+49 5.685E+49 756.4579 4.407E+100 1.535E+99 28.7150

lusishun · 发表于 2026-6-8 08:21

鲁思顺的偶数哥猜素数对存在公式的数值，不知道有价值与否。

cuikun-186 · 发表于 2026-6-8 09:15

本帖最后由 cuikun-186 于 2026-6-8 09:46 编辑

杨老师好！

联乘积偶数P#的哥猜表法数是区间[6，P#-1]内最大的，即r2(P#)最大。

杨老师能否给出更大的联乘积偶数P#的哥猜表法数r2(P#)的真值？

yangchuanju · 发表于 2026-6-8 12:29

cuikun-186 发表于 2026-6-8 09:15
杨老师好！

联乘积偶数P#的哥猜表法数是区间[6，P#-1]内最大的，即r2(P#)最大。

p p# A116979
2 2 1 0
3 6 2 1
5 30 3 3
7 210 4 19
11 2310 5 114
13 30030 6 905
17 510510 7 9493
19 9699690 8 124180
23 223092870 9 2044847
29 6469693230 10 43755729
31 2.0056E+11 11 1043468386
37 7.42074E+12 12 30309948241

yangchuanju · 发表于 2026-6-8 12:34

几组不同偶数的哥猜连乘积——随着偶数的不断增大，连乘积计算式的误差逐渐增大：
—— 偶数最大素数连乘积波动因子单哥猜数连乘哥数连乘/哥数哈李/哥数
序数 10的幂数
1 10 3 0.3333 1.3333 2 1.11 0.5556 0.8301
2 100 7 0.1429 1.3333 6 4.76 0.7937 0.6917
3 1000 31 0.0621 1.3333 28 20.70 0.7392 0.6588
4 10000 97 0.0383 1.3333 127 127.66 1.0052 0.8170
5 100000 313 0.0246 1.3333 810 820.39 1.0128 0.8198
6 1000000 997 0.0173 1.3333 5402 5770.88 1.0683 0.8537
7 10000000 3137 0.0128 1.3333 38807 42642.3 1.0988 0.8731
8 100000000 9973 0.0098 1.3333 291400 326294.4 1.1197 0.8902
9 1000000000 31607 0.0077 1.3333 2274205 2582599.6 1.1356 0.9012
10 10000000000 99991 0.0063 1.3333 18200488 20921398.5 1.1495 0.9122
11 1E+11 316223 0.0052 1.3333 149091160 172979150.7 1.1602 0.9203
12 1E+12 999983 0.0044 1.3333 1243722370 1453644840 1.1688 0.9270
13 1E+13 3162277 0.0037 1.3333 10533150855 12386409457 1.1759 0.9326
14 1E+14 9999991 0.0032 1.3333 90350630388 1.06805E+11 1.1821 0.9375
15 1E+15 31622743 0.0028 1.3333 783538341852 9.30385E+11 1.1874 0.9417
16 1E+16 99999989 0.0025 1.3333 6852674128787 8.17732E+12 1.1933 0.9464
2的幂数
1 2 1 1 1 0 0.50 —— ——
2 4 1 1 1 1 1.00 1 1.3740
3 8 1 1 1 1 2.00 2 1.2214
4 16 3 0.3333 1 2 1.33 0.6667 0.6870
5 32 5 0.2000 1 2 1.60 0.8000 0.8794
6 64 7 0.1429 1 5 2.29 0.4571 0.4885
7 128 11 0.1169 1 3 3.74 1.2468 1.1964
8 256 13 0.0989 1 8 6.33 0.7912 0.6870
9 512 19 0.0781 1 11 9.99 0.9086 0.7896
10 1024 31 0.0621 1 22 15.90 0.7225 0.6396
11 2048 43 0.0533 1 25 27.27 1.0910 0.9303
12 4096 61 0.0459 1 53 46.96 0.8861 0.7374
13 8192 89 0.0391 1 76 80.08 1.0537 0.8764
14 16384 127 0.0343 1 151 140.42 0.9300 0.7607
15 32768 181 0.0297 1 244 243.52 0.9980 0.8201
16 65536 251 0.0266 1 435 435.97 1.0022 0.8086
17 131072 359 0.0236 1 749 773.97 1.0333 0.8320
18 262144 509 0.0210 1 1314 1379.05 1.0495 0.8461
19 524288 719 0.0190 1 2367 2492.87 1.0532 0.8431
20 1048576 1021 0.0172 1 4239 4502.75 1.0622 0.8497
21 2097152 1447 0.0156 1 7471 8199.61 1.0975 0.8746
22 4194304 2039 0.0142 1 13705 14940.18 1.0901 0.8688
23 8388608 2887 0.0130 1 24928 27332.03 1.0964 0.8741
24 16777216 4093 0.0120 1 45746 50250.88 1.0985 0.8749
25 33554432 5791 0.0111 1 83467 92768.98 1.1114 0.8838
26 67108864 8191 0.0102 1 153850 171677.74 1.1159 0.8866
27 134217728 11579 0.0095 1 283746 318591.20 1.1228 0.8916
28 268435456 16381 0.0088 1 525236 592129.21 1.1274 0.8957
29 536870912 23167 0.0082 1 975685 1104308.73 1.1318 0.8990
30 1073741824 32749 0.0077 1 1817111 2065494.79 1.1367 0.9021
31 2147483648 46337 0.0072 1 3390038 3869035.92 1.1413 0.9057
32 4294967296 65521 0.0068 1 6341424 7263389.60 1.1454 0.9088
33 8589934592 92681 0.0064 1 11891654 13658932.7 1.1486 0.9114
34 17179869184 131071 0.0060 1 22336060 25737053.3 1.1523 0.9142
35 34359738368 185363 0.0057 1 42034097 48581542.3 1.1558 0.9169
36 68719476736 262139 0.0053 1 79287664 91848700.0 1.1584 0.9189
37 1.37439E+11 370723 0.0051 1 149711134 173898027.1 1.1616 0.9214
38 2.74878E+11 524287 0.0048 1 283277225 329731632.5 1.1640 0.9233
39 5.49756E+11 741431 0.0046 1 536710100 626130752.0 1.1666 0.9253
40 1.09951E+12 1048573 0.0043 1 1018369893 1190494225.7 1.1690 0.9272
p#
2 2 1 1 1 0 0.50 —— ——
3 6 1 1 1 1 1.50 1.5000 1.2338
5 30 5 0.2 2.666666667 3 4.00 1.3333 1.5218
7 210 13 0.0989 3.2 19 16.62 0.8745 0.8166
11 2310 47 0.0510 3.555555556 114 104.73 0.9187 0.7929
13 30030 173 0.0304 3.878787879 905 885.18 0.9781 0.7994
17 510510 709 0.0191 4.137373737 9493 10070.92 1.0609 0.8503
19 9699690 3109 0.0128 4.380748663 124180 136157.57 1.0965 0.8728
23 223092870 14929 0.0090 4.589355742 2044847 2302808.4 1.1262 0.8945
29 6469693230 80429 0.0065 4.759331881 43755729 50200067.0 1.1473 0.9103
31 2.0056E+11 447829 0.0049 4.923446773 1043468386 1213390098.8 1.1628 0.9224
37 7.42074E+12 2734099 0.0038 5.064116681 30309948241 35598549191.1 1.1745 0.9320
n!
1 1 1 1 1 0 0.25 —— ——
2 2 1 1 1 0 0.50 —— ——
3 6 1 1 1 1 1.50 1.5000 1.2338
4 24 3 0.3333 2 3 4.00 1.3333 1.0458
5 120 7 0.1429 2.6667 12 11.43 0.9524 0.7681
6 720 23 0.0713 2.6667 39 34.22 0.8774 0.7508
7 5040 67 0.0445 3.2000 184 179.39 0.9750 0.7962
8 40320 199 0.0285 3.2000 951 920.10 0.9675 0.7964
9 362880 601 0.0201 3.2000 5531 5833.12 1.0546 0.8457
10 3628800 1901 0.0145 3.2000 38713 42122.38 1.0881 0.8680
11 39916800 6317 0.0108 3.5556 346207 384431.58 1.1104 0.8835
12 479001600 21881 0.0083 3.5556 3130812 3543861.66 1.1319 0.8989
13 6227020800 78901 0.0065 3.8788 34444964 39509420.8 1.1470 0.9102
14 87178291200 295259 0.0052 3.8788 382437428 443476810.1 1.1596 0.9198
15 1.30767E+12 1143529 0.0043 3.8788 4637235145 5423905489.1 1.1696 0.9277

yangchuanju · 发表于 2026-6-8 12:40

2p型偶数
p 2p 根内最大素数连乘积波动因子单计哥猜数连乘哥数连乘/哥数哈李/哥数
2 4 1 1 1 1 1.00 1.0000 1.3740
3 6 1 1 1 1 1.50 1.5000 1.2338
5 10 3 0.3333 1 2 0.83 0.4167 0.6226
7 14 3 0.3333 1 2 1.17 0.5833 0.6635
11 22 3 0.3333 1 3 1.83 0.6111 0.5067
13 26 5 0.2000 1 3 1.30 0.4333 0.5390
17 34 5 0.2000 1 4 1.70 0.4250 0.4512
19 38 5 0.2000 1 2 1.90 0.9500 0.9479
23 46 5 0.2000 1 4 2.30 0.5750 0.5179
29 58 7 0.1429 1 4 2.07 0.5179 0.5806
31 62 7 0.1429 1 3 2.21 0.7381 0.8010
37 74 7 0.1429 1 5 2.64 0.5286 0.5274
41 82 7 0.1429 1 5 2.93 0.5857 0.5575
43 86 7 0.1429 1 5 3.07 0.6143 0.5723
47 94 7 0.1429 1 5 3.36 0.6714 0.6013
53 106 7 0.1429 1 6 3.79 0.6310 0.5363
59 118 7 0.1429 1 6 4.21 0.7024 0.5705
61 122 11 0.1169 1 4 3.56 0.8912 0.8724
67 134 11 0.1169 1 6 3.92 0.6526 0.6146
71 142 11 0.1169 1 8 0.0000 0.4771
73 146 11 0.1169 1 6 4.27 0.7110 0.6468
79 158 11 0.1169 1 5 4.62 0.9234 0.8139
83 166 11 0.1169 1 6 4.85 0.8084 0.6989
89 178 13 0.0989 1 7 4.40 0.6287 0.6252
97 194 13 0.0989 1 7 4.80 0.6852 0.6593
101 202 13 0.0989 1 9 4.99 0.5549 0.5258
103 206 13 0.0989 1 7 5.09 0.7276 0.6844
107 214 13 0.0989 1 8 5.29 0.6614 0.6133
109 218 13 0.0989 1 7 5.39 0.7700 0.7091
113 226 13 0.0989 1 7 5.59 0.7983 0.7254
127 254 13 0.0989 1 9 6.28 0.6978 0.6076
131 262 13 0.0989 1 9 6.48 0.7198 0.6198
137 274 13 0.0989 1 11 6.77 0.6159 0.5219
139 278 13 0.0989 1 7 6.87 0.9819 0.8278
149 298 17 0.0873 1 11 6.50 0.5910 0.5510
151 302 17 0.0873 1 9 6.59 0.7321 0.6793
157 314 17 0.0873 1 9 6.85 0.7612 0.6968
163 326 17 0.0873 1 7 7.11 1.0160 0.9181
167 334 17 0.0873 1 11 7.29 0.6624 0.5936
173 346 17 0.0873 1 9 7.55 0.8387 0.7425
179 358 17 0.0873 1 10 7.81 0.7810 0.6834
181 362 19 0.0781 1 8 7.07 0.8833 0.8606
191 382 19 0.0781 1 10 7.46 0.7457 0.7134
193 386 19 0.0781 1 12 7.53 0.6279 0.5986
197 394 19 0.0781 1 11 7.69 0.6992 0.6620
199 398 19 0.0781 1 7 7.77 1.1098 1.0474
211 422 19 0.0781 1 11 8.24 0.7489 0.6931
223 446 19 0.0781 1 12 8.71 0.7255 0.6593
227 454 19 0.0781 1 12 8.86 0.7385 0.6673
229 458 19 0.0781 1 9 8.94 0.9933 0.8949
233 466 19 0.0781 1 13 9.10 0.6997 0.6269
239 478 19 0.0781 1 11 9.33 0.8482 0.7537
241 482 19 0.0781 1 11 9.41 0.8553 0.7579
251 502 19 0.0781 1 15 9.80 0.6533 0.5713
257 514 19 0.0781 1 14 10.03 0.7167 0.6220
263 526 19 0.0781 1 15 10.27 0.6845 0.5897
269 538 23 0.0713 1 14 9.59 0.6849 0.6417
271 542 23 0.0713 1 10 9.66 0.9660 0.9029
277 554 23 0.0713 1 11 9.87 0.8976 0.8331
281 562 23 0.0713 1 14 10.02 0.7154 0.6611
283 566 23 0.0713 1 13 10.09 0.7760 0.7154
293 586 23 0.0713 1 13 10.44 0.8034 0.7326
307 614 23 0.0713 1 15 10.94 0.7295 0.6556
311 622 23 0.0713 1 17 11.09 0.6521 0.5837
313 626 23 0.0713 1 12 11.16 0.9297 0.8305
317 634 23 0.0713 1 14 11.30 0.8071 0.7182
331 662 23 0.0713 1 14 11.80 0.8428 0.7399
337 674 23 0.0713 1 15 12.01 0.8008 0.6992
347 694 23 0.0713 1 19 12.37 0.6510 0.5633
349 698 23 0.0713 1 14 12.44 0.8886 0.7676
353 706 23 0.0713 1 19 12.58 0.6622 0.5701
359 718 23 0.0713 1 15 12.80 0.8531 0.7306
367 734 23 0.0713 1 15 13.08 0.8721 0.7419
373 746 23 0.0713 1 18 13.30 0.7386 0.6253
379 758 23 0.0713 1 15 13.51 0.9006 0.7588
383 766 23 0.0713 1 17 13.65 0.8031 0.6744
389 778 23 0.0713 1 15 13.87 0.9244 0.7727
397 794 23 0.0713 1 17 14.15 0.8324 0.6916
401 802 23 0.0713 1 16 14.29 0.8934 0.7400
409 818 23 0.0713 1 17 14.58 0.8576 0.7062
419 838 23 0.0713 1 17 14.94 0.8785 0.7183
421 842 29 0.0664 1 18 13.97 0.7762 0.6806
431 862 29 0.0664 1 17 14.30 0.8414 0.7327
433 866 29 0.0664 1 17 14.37 0.8453 0.7351
439 878 29 0.0664 1 14 14.57 1.0406 0.9013
443 886 29 0.0664 1 18 14.70 0.8168 0.7055
449 898 29 0.0664 1 19 14.90 0.7843 0.6747
457 914 29 0.0664 1 20 15.17 0.7583 0.6490
461 922 29 0.0664 1 20 15.30 0.7650 0.6531
463 926 29 0.0664 1 18 15.37 0.8536 0.7278
467 934 29 0.0664 1 20 15.50 0.7749 0.6591
479 958 29 0.0664 1 22 15.90 0.7226 0.6100
487 974 31 0.0621 1 17 15.12 0.8894 0.7987
491 982 31 0.0621 1 17 15.24 0.8967 0.8034
499 998 31 0.0621 1 17 15.49 0.9113 0.8127
503 1006 31 0.0621 1 18 15.62 0.8676 0.7719
509 1018 31 0.0621 1 20 15.80 0.7901 0.7006
521 1042 31 0.0621 1 22 16.17 0.7352 0.6475
523 1046 31 0.0621 1 19 16.24 0.8546 0.7518
541 1082 31 0.0621 1 20 16.80 0.8398 0.7317
547 1094 31 0.0621 1 23 16.98 0.7383 0.6413
557 1114 31 0.0621 1 23 17.29 0.7518 0.6496
563 1126 31 0.0621 1 23 17.48 0.7599 0.6546
569 1138 31 0.0621 1 20 17.67 0.8833 0.7585
571 1142 31 0.0621 1 18 17.73 0.9848 0.8450
577 1154 31 0.0621 1 19 17.91 0.9428 0.8065
587 1174 31 0.0621 1 22 18.22 0.8284 0.7052
593 1186 31 0.0621 1 20 18.41 0.9205 0.7813
599 1198 31 0.0621 1 24 18.60 0.7749 0.6558
601 1202 31 0.0621 1 19 18.66 0.9820 0.8304
607 1214 31 0.0621 1 22 18.84 0.8566 0.7223
613 1226 31 0.0621 1 22 19.03 0.8650 0.7274
617 1234 31 0.0621 1 25 19.16 0.7662 0.6431
619 1238 31 0.0621 1 18 19.22 1.0676 0.8953
631 1262 31 0.0621 1 22 19.59 0.8904 0.7427
641 1282 31 0.0621 1 26 19.90 0.7654 0.6356
643 1286 31 0.0621 1 22 19.96 0.9074 0.7529
647 1294 31 0.0621 1 26 20.09 0.7726 0.6399
653 1306 31 0.0621 1 24 20.27 0.8447 0.6979
659 1318 31 0.0621 1 26 20.46 0.7869 0.6484
661 1322 31 0.0621 1 21 20.52 0.9772 0.8046
673 1346 31 0.0621 1 25 20.89 0.8358 0.6847
677 1354 31 0.0621 1 21 21.02 1.0009 0.8186
683 1366 31 0.0621 1 27 21.20 0.7853 0.6408
691 1382 37 0.0587 1 20 20.29 1.0147 0.8724
701 1402 37 0.0587 1 27 20.59 0.7625 0.6529
709 1418 37 0.0587 1 20 20.82 1.0411 0.8888
719 1438 37 0.0587 1 23 21.12 0.9181 0.7807
727 1454 37 0.0587 1 26 21.35 0.8212 0.6962
733 1466 37 0.0587 1 25 21.53 0.8611 0.7284
739 1478 37 0.0587 1 26 21.70 0.8347 0.7045
743 1486 37 0.0587 1 25 21.82 0.8728 0.7356
751 1502 37 0.0587 1 27 22.06 0.8169 0.6864
757 1514 37 0.0587 1 23 22.23 0.9666 0.8105
761 1522 37 0.0587 1 27 22.35 0.8277 0.6930
769 1538 37 0.0587 1 26 22.58 0.8686 0.7252
773 1546 37 0.0587 1 30 22.70 0.7567 0.6309
787 1574 37 0.0587 1 23 23.11 1.0049 0.8337
797 1594 37 0.0587 1 27 23.41 0.8669 0.7168
809 1618 37 0.0587 1 32 23.76 0.7424 0.6114
811 1622 37 0.0587 1 24 23.82 0.9924 0.8166
821 1642 37 0.0587 1 27 24.11 0.8930 0.7324
823 1646 37 0.0587 1 26 24.17 0.9296 0.7620
827 1654 37 0.0587 1 31 24.29 0.7835 0.6413
829 1658 37 0.0587 1 27 24.35 0.9017 0.7376
839 1678 37 0.0587 1 31 24.64 0.7948 0.6481
853 1706 41 0.0559 1 30 23.83 0.7943 0.6779
857 1714 41 0.0559 1 27 23.94 0.8867 0.7558
859 1718 41 0.0559 1 21 24.00 1.1427 0.9733
863 1726 41 0.0559 1 31 24.11 0.7777 0.6616
877 1754 41 0.0559 1 27 24.50 0.9074 0.7686
881 1762 41 0.0559 1 29 24.61 0.8486 0.7180
883 1766 41 0.0559 1 32 24.67 0.7708 0.6518
887 1774 41 0.0559 1 27 24.78 0.9177 0.7750
907 1814 41 0.0559 1 28 25.34 0.9049 0.7597
911 1822 41 0.0559 1 27 25.45 0.9425 0.7904
919 1838 41 0.0559 1 28 25.67 0.9169 0.7670
929 1858 43 0.0533 1 29 24.74 0.8533 0.7465
937 1874 43 0.0533 1 30 24.96 0.8319 0.7262
941 1882 43 0.0533 1 33 25.06 0.7595 0.6622
947 1894 43 0.0533 1 32 25.22 0.7883 0.6861
953 1906 43 0.0533 1 30 25.38 0.8461 0.7353
967 1934 43 0.0533 1 28 25.76 0.9199 0.7963
971 1942 43 0.0533 1 30 25.86 0.8621 0.7454
977 1954 43 0.0533 1 35 26.02 0.7435 0.6419
983 1966 43 0.0533 1 29 26.18 0.9029 0.7782
991 1982 43 0.0533 1 30 26.40 0.8799 0.7567
997 1994 43 0.0533 1 27 26.56 0.9835 0.8445

cuikun-186 · 发表于 2026-6-8 14:46

yangchuanju 发表于 2026-6-8 12:29
p p# A116979
2 2 1 0
3 6 2 1

杨老师你好，麻烦你再给出：不超过P#的π(P#)；例如π(6)=3，π(30)=10，π(210)=46，π(2310)=343，

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