欧拉常数及其在求素数个数、哥猜素数对中的应用

yangchuanju · 发表于 2026-8-12 07:14

本帖最后由 yangchuanju 于 2026-8-12 07:24 编辑

素数连乘积小偶数大偶数小偶连乘哥数大偶连乘哥数小偶对数哥数大偶对数哥数小偶比大偶比
2 0.5000 4 8 0.50 1.00 1.37 1.22 0.3639 0.8188
3 0.3333 10 24 0.83 2.00 1.25 1.57 0.6693 1.2749
5 0.2000 26 48 1.30 2.40 1.62 2.11 0.8040 1.1350
7 0.1429 50 120 1.79 4.29 2.16 3.46 0.8279 1.2400
11 0.1169 122 168 3.56 4.91 3.49 4.22 1.0215 1.1621
13 0.0989 170 288 4.20 7.12 4.25 5.93 0.9879 1.2011
17 0.0873 290 360 6.33 7.85 5.96 6.86 1.0624 1.1450
19 0.0781 362 528 7.07 10.31 6.88 8.87 1.0264 1.1621
23 0.0713 530 840 9.45 14.97 8.89 12.23 1.0623 1.2240
29 0.0664 842 960 13.97 15.93 12.25 13.44 1.1404 1.1853
31 0.0621 962 1368 14.93 21.24 13.46 17.32 1.1095 1.2261
37 0.0587 1370 1680 20.12 24.67 17.34 20.11 1.1603 1.2268
41 0.0559 1682 1848 23.49 25.81 20.13 21.56 1.1673 1.1971
43 0.0533 1850 2208 24.64 29.41 21.58 24.59 1.1417 1.1960
47 0.0510 2210 2808 28.18 35.81 24.60 29.40 1.1454 1.2178
53 0.0491 2810 3480 34.48 42.70 29.42 34.55 1.1720 1.2360
59 0.0474 3482 3720 41.28 44.10 34.56 36.33 1.1943 1.2137
61 0.0459 3722 4488 42.67 51.46 36.35 41.90 1.1741 1.2281
67 0.0445 4490 5040 49.94 56.06 41.91 45.78 1.1916 1.2246
71 0.0432 5042 5328 54.50 57.59 45.79 47.77 1.1902 1.2056
73 0.0421 5330 6240 56.04 65.61 47.78 53.94 1.1727 1.2162
79 0.0410 6242 6888 63.96 70.58 53.96 58.22 1.1855 1.2124
83 0.0400 6890 7920 68.90 79.20 58.23 64.88 1.1832 1.2208
89 0.0391 7922 9408 77.44 91.97 64.89 74.19 1.1934 1.2396
97 0.0383 9410 10200 90.09 97.66 74.21 79.04 1.2141 1.2356
101 0.0375 10202 10608 95.74 99.55 79.05 81.50 1.2112 1.2214
103 0.0368 10610 11448 97.64 105.35 81.52 86.53 1.1978 1.2175
107 0.0361 11450 11880 103.40 107.28 86.54 89.09 1.1948 1.2042
109 0.0355 11882 12768 105.33 113.18 89.10 94.29 1.1822 1.2004
113 0.0348 12770 16128 111.20 140.44 94.30 113.43 1.1792 1.2381
127 0.0343 16130 17160 138.25 147.07 113.44 119.16 1.2186 1.2343
131 0.0338 17162 18768 144.84 158.40 119.17 127.96 1.2154 1.2378
137 0.0333 18770 19320 156.10 160.68 127.97 130.95 1.2198 1.2270
139 0.0328 19322 22200 158.38 181.97 130.97 146.33 1.2093 1.2436
149 0.0323 22202 22800 179.55 184.38 146.34 149.48 1.2269 1.2335
151 0.0319 22802 24648 181.96 196.69 149.49 159.12 1.2172 1.2361
157 0.0315 24650 26568 194.20 209.31 159.13 169.00 1.2204 1.2385
163 0.0311 26570 27888 206.76 217.01 169.01 175.72 1.2234 1.2350
167 0.0308 27890 29928 214.43 230.10 175.73 186.00 1.2202 1.2371
173 0.0304 29930 32040 227.45 243.49 186.01 196.51 1.2228 1.2390
179 0.0301 32042 32760 240.78 246.18 196.52 200.07 1.2252 1.2305
181 0.0297 32762 36480 243.47 271.10 200.08 218.25 1.2169 1.2422
191 0.0294 36482 37248 268.28 273.91 218.26 221.96 1.2292 1.2340
193 0.0291 37250 38808 271.09 282.42 221.97 229.47 1.2213 1.2308
197 0.0288 38810 39600 279.57 285.26 229.48 233.26 1.2183 1.2230
199 0.0285 39602 44520 282.41 317.48 233.27 256.53 1.2107 1.2376
211 0.0283 44522 49728 314.49 351.26 256.54 280.71 1.2259 1.2513
223 0.0280 49730 51528 348.12 360.71 280.72 288.96 1.2401 1.2483
227 0.0278 51530 52440 357.55 363.86 288.97 293.13 1.2373 1.2413
229 0.0275 52442 54288 360.70 373.39 293.14 301.53 1.2305 1.2383
233 0.0273 54290 57120 370.20 389.50 301.54 314.33 1.2277 1.2392
239 0.0270 57122 58080 386.25 392.73 314.33 318.64 1.2288 1.2325
241 0.0268 58082 63000 389.48 422.46 318.65 340.56 1.2223 1.2405
251 0.0266 63002 66048 419.11 439.37 340.57 354.01 1.2306 1.2411
257 0.0264 66050 69168 435.97 456.55 354.01 367.66 1.2315 1.2418
263 0.0262 69170 72360 453.09 473.99 367.67 381.54 1.2323 1.2423
269 0.0260 72362 73440 470.47 477.48 381.54 386.21 1.2331 1.2363
271 0.0258 73442 76728 473.97 495.18 386.22 400.36 1.2272 1.2368
277 0.0256 76730 78960 491.62 505.90 400.37 409.91 1.2279 1.2342
281 0.0254 78962 80088 502.32 509.48 409.92 414.73 1.2254 1.2285
283 0.0253 80090 85848 505.89 542.26 414.74 439.14 1.2198 1.2348
293 0.0251 85850 94248 538.57 591.26 439.14 474.28 1.2264 1.2466
307 0.0249 94250 96720 587.42 602.81 474.29 484.52 1.2385 1.2441
311 0.0248 96722 97968 598.95 606.66 484.53 489.68 1.2361 1.2389
313 0.0246 97970 100488 602.80 618.29 489.69 500.06 1.2310 1.2364
317 0.0245 100490 109560 614.40 669.86 500.07 537.12 1.2286 1.2471
331 0.0243 109562 113568 665.82 690.17 537.13 553.34 1.2396 1.2473
337 0.0242 113570 120408 686.08 727.39 553.34 580.81 1.2399 1.2524
347 0.0240 120410 121800 723.21 731.56 580.82 586.37 1.2452 1.2476
349 0.0239 121802 124608 727.38 744.14 586.38 597.56 1.2405 1.2453
353 0.0238 124610 128880 739.93 765.29 597.57 614.51 1.2382 1.2454
359 0.0236 128882 134688 761.04 795.32 614.52 637.42 1.2384 1.2477
367 0.0235 134690 139128 791.00 817.06 637.43 654.83 1.2409 1.2477
373 0.0234 139130 143640 812.69 839.04 654.84 672.44 1.2411 1.2477
379 0.0232 143642 146688 834.62 852.32 672.45 684.29 1.2412 1.2456
383 0.0231 146690 151320 847.88 874.64 684.30 702.22 1.2391 1.2455
389 0.0230 151322 157608 870.16 906.30 702.23 726.43 1.2391 1.2476
397 0.0229 157610 160800 901.75 920.00 726.44 738.67 1.2413 1.2455
401 0.0228 160802 167280 915.42 952.30 738.68 763.39 1.2393 1.2475
409 0.0227 167282 175560 947.66 994.55 763.40 794.78 1.2414 1.2513
419 0.0226 175562 177240 989.82 999.28 794.79 801.12 1.2454 1.2473
421 0.0224 177242 185760 994.54 1042.34 801.13 833.15 1.2414 1.2511
431 0.0223 185762 187488 1037.51 1047.15 833.16 839.62 1.2453 1.2472
433 0.0222 187490 192720 1042.32 1071.40 839.62 859.15 1.2414 1.2470
439 0.0221 192722 196248 1066.53 1086.04 859.16 872.27 1.2414 1.2451
443 0.0220 196250 201600 1081.15 1110.62 872.28 892.12 1.2395 1.2449
449 0.0219 201602 208848 1105.69 1145.43 892.13 918.87 1.2394 1.2466
457 0.0218 208850 212520 1140.43 1160.47 918.88 932.37 1.2411 1.2446
461 0.0217 212522 214368 1155.44 1165.48 932.38 939.15 1.2392 1.2410
463 0.0217 214370 218088 1160.46 1180.58 939.16 952.78 1.2356 1.2391
467 0.0216 218090 220000 1175.54 1236.72 952.78 994.15 1.2338 1.2440

yangchuanju · 发表于 2026-8-12 07:18

本帖最后由 yangchuanju 于 2026-8-12 07:20 编辑

（接上表）
素数小偶数大偶数小偶哥猜大偶哥猜小偶波因大偶波因小偶连乘/真哥大偶连乘/真哥小偶对数/真哥大偶对数/真哥
2 4 8 1 1 1.0000 1.0000 0.5000 1.0000 1.3740 1.2214
3 10 24 2 3 1.0000 2.0000 0.4167 1.3333 0.6226 1.0458
5 26 48 3 5 1.0000 2.0000 0.4333 0.9600 0.5390 0.8458
7 50 120 4 12 1.3333 2.6667 0.5952 0.9524 0.7189 0.7681
11 122 168 4 13 1.0000 2.4000 0.8912 0.9063 0.8724 0.7799
13 170 288 9 17 1.3333 2.0000 0.6227 0.8378 0.6303 0.6975
17 290 360 10 22 1.3333 2.6667 0.8436 0.9520 0.7940 0.8315
19 362 528 8 25 1.0000 2.2222 0.8833 0.9161 0.8606 0.7884
23 530 840 14 51 1.3333 3.2000 0.8996 0.9394 0.8468 0.7674
29 842 960 18 45 1.0000 2.6667 0.7762 0.9440 0.6806 0.7964
31 962 1368 16 48 1.0909 2.1176 1.0182 0.9369 0.9177 0.7641
37 1370 1680 28 83 1.3333 3.2000 0.9579 0.9511 0.8256 0.7753
41 1682 1848 24 70 1.0370 2.6667 1.0151 0.9833 0.8697 0.8214
43 1850 2208 38 60 1.3714 2.0952 0.8892 1.0269 0.7788 0.8586
47 2210 2808 47 90 1.5515 2.1818 0.9303 0.8680 0.8121 0.7128
53 2810 3480 51 123 1.3333 2.7654 0.9014 0.9600 0.7691 0.7767
59 3482 3720 45 128 1.0000 2.7586 0.9172 0.9504 0.7680 0.7830
61 3722 4488 50 127 1.0000 2.3704 0.8535 0.9604 0.7269 0.7820
67 4490 5040 71 184 1.3333 3.2000 0.9379 0.9750 0.7871 0.7962
71 5042 5328 59 126 1.0000 2.0571 0.9238 0.9403 0.7762 0.7799
73 5330 6240 86 198 1.4918 2.9091 0.9721 0.9639 0.8289 0.7926
79 6242 6888 66 178 1.0000 2.4615 0.9692 0.9761 0.8175 0.8051
83 6890 7920 117 243 1.4831 2.9630 0.8734 0.9658 0.7382 0.7911
89 7922 9408 78 223 1.0667 2.4000 1.0591 0.9898 0.8874 0.7985
97 9410 10200 125 294 1.3333 2.8444 0.9610 0.9448 0.7915 0.7647
101 10202 10608 98 241 1.0000 2.3273 0.9770 0.9614 0.8066 0.7871
103 10610 11448 137 213 1.3333 2.0392 0.9502 1.0086 0.7934 0.8284
107 11450 11880 140 327 1.3333 2.9630 0.9847 0.9721 0.8242 0.8072
109 11882 12768 121 302 1.0909 2.5412 0.9496 0.9524 0.8033 0.7934
113 12770 16128 153 344 1.3333 2.4000 0.9691 0.9798 0.8218 0.7914
127 16130 17160 186 480 1.3333 3.2323 0.9910 0.9904 0.8132 0.8024
131 17162 18768 138 356 1.0000 2.2349 1.0496 0.9944 0.8636 0.8033
137 18770 19320 199 539 1.3333 3.3524 1.0459 0.9994 0.8574 0.8145
139 19322 22200 155 506 1.0000 2.7429 1.0218 0.9864 0.8449 0.7932
149 22202 22800 200 523 1.0667 2.8235 0.9576 0.9954 0.7805 0.8070
151 22802 24648 196 435 1.0909 2.2102 1.0127 0.9993 0.8321 0.8084
157 24650 26568 286 426 1.4749 2.0513 1.0015 1.0079 0.8206 0.8138
163 26570 27888 280 526 1.3333 2.4296 0.9845 1.0024 0.8048 0.8116
167 27890 29928 283 478 1.3333 2.1247 1.0103 1.0228 0.8279 0.8267
173 29930 32040 307 648 1.3868 2.6973 1.0274 1.0135 0.8402 0.8180
179 32042 32760 236 857 1.0286 3.4909 1.0494 1.0028 0.8565 0.8150
181 32762 36480 242 762 1.0000 2.8235 1.0061 1.0045 0.8268 0.8087
191 36482 37248 287 553 1.1378 2.0211 1.0636 1.0011 0.8653 0.8112
193 37250 38808 360 750 1.3424 2.6667 1.0109 1.0042 0.8277 0.8159
197 38810 39600 386 852 1.3333 2.9630 0.9657 0.9920 0.7927 0.8112
199 39602 44520 291 1008 1.0000 3.2627 0.9705 1.0276 0.8016 0.8303
211 44522 49728 313 838 1.0142 2.4686 1.0190 1.0347 0.8312 0.8269
223 49730 51528 444 743 1.3333 2.1367 1.0454 1.0373 0.8430 0.8310
227 51530 52440 466 1045 1.3333 2.9580 1.0230 1.0299 0.8268 0.8297
229 52442 54288 372 840 1.0909 2.2626 1.0578 1.0058 0.8596 0.8122
233 54290 57120 516 1330 1.3715 3.4133 0.9840 0.9996 0.8015 0.8067
239 57122 58080 406 1155 1.0909 2.9630 1.0378 1.0075 0.8446 0.8174
241 58082 63000 386 1339 1.0090 3.2000 1.0181 1.0096 0.8329 0.8139
251 63002 66048 440 880 1.0766 2.0488 1.0255 1.0229 0.8333 0.8242
257 66050 69168 570 998 1.3333 2.2394 1.0198 1.0245 0.8281 0.8250
263 69170 72360 579 1247 1.3333 2.7077 1.0434 1.0292 0.8467 0.8285
269 72362 73440 475 1349 1.0105 2.8444 1.0009 1.0068 0.8117 0.8143
271 73442 76728 464 1031 1.0000 2.1105 1.0215 1.0137 0.8324 0.8196
277 76730 78960 636 1630 1.3333 3.2711 1.0306 1.0153 0.8393 0.8226
281 78962 80088 542 1056 1.0909 2.0741 1.0110 1.0007 0.8251 0.8146
283 80090 85848 664 1289 1.3333 2.4338 1.0158 1.0239 0.8328 0.8291
293 85850 94248 764 1636 1.4366 2.8444 1.0127 1.0280 0.8257 0.8246
307 94250 96720 879 1756 1.5084 3.0094 1.0080 1.0331 0.8139 0.8304
311 96722 97968 592 1284 1.0074 2.1959 1.0192 1.0375 0.8245 0.8375
313 97970 100488 789 1253 1.3610 2.0657 1.0398 1.0193 0.8447 0.8244
317 100490 109560 885 1954 1.4545 2.9995 1.0098 1.0283 0.8219 0.8245
331 109562 113568 665 1739 1.0370 2.6182 1.0383 1.0391 0.8376 0.8331
337 113570 120408 894 1428 1.3725 2.0862 1.0533 1.0627 0.8495 0.8485
347 120410 121800 929 2358 1.3333 3.3185 1.0380 1.0296 0.8336 0.8252
349 121802 124608 728 1619 1.0000 2.2612 0.9991 1.0393 0.8055 0.8346
353 124610 128880 1011 1970 1.4222 2.6817 1.0409 1.0418 0.8406 0.8365
359 128882 134688 776 1656 1.0909 2.1308 1.0699 1.0233 0.8639 0.8202
367 134690 139128 989 1950 1.3333 2.4521 1.0664 1.0274 0.8594 0.8234
373 139130 143640 1030 2718 1.3333 3.3882 1.0520 1.0459 0.8477 0.8383
379 143642 146688 790 1682 1.0000 2.0106 1.0565 1.0188 0.8512 0.8180
383 146690 151320 1084 2501 1.3333 2.9397 1.0429 1.0281 0.8417 0.8254
389 151322 157608 857 1955 1.0370 2.2335 1.0530 1.0354 0.8498 0.8299
397 157610 160800 1164 2374 1.3333 2.7077 1.0329 1.0493 0.8321 0.8425
401 160802 167280 937 2698 1.0756 2.9174 1.0509 1.0297 0.8480 0.8255
409 167282 175560 922 3570 1.0000 3.7647 1.0278 1.0488 0.8280 0.8381
419 175562 177240 949 3118 1.0256 3.2153 1.0698 1.0305 0.8590 0.8261
421 177242 185760 1107 2750 1.1666 2.7317 1.0480 1.0354 0.8442 0.8276
431 185762 187488 1029 2524 1.0066 2.4828 1.0149 1.0300 0.8150 0.8259
433 187490 192720 1340 3094 1.3333 3.0047 1.0371 1.0405 0.8354 0.8343
439 192722 196248 997 2464 1.0058 2.3938 1.0760 1.0551 0.8668 0.8474
443 196250 201600 1409 3390 1.3419 3.2000 1.0297 1.0484 0.8308 0.8421
449 201602 208848 1075 2277 1.0000 2.1270 1.0285 1.0700 0.8299 0.8583
457 208850 212520 1480 4210 1.3333 3.7249 1.0274 1.0267 0.8278 0.8249
461 212522 214368 1086 3115 1.0000 2.7654 1.0639 1.0347 0.8585 0.8338
463 214370 218088 1744 2481 1.5678 2.1913 1.0432 1.0427 0.8443 0.8415
467 218090 229440 1539 1722 1.3524 1.4815 1.0330 1.0640 0.8373 0.8553
—— ——— ——— —— —— —— 最大 1.0760 1.0700 0.9177 0.8586

yangchuanju · 发表于 2026-8-12 11:10

本帖最后由 yangchuanju 于 2026-8-12 16:18 编辑

特定大偶数N的哥猜素数对下限公式
大偶数N的单计哥猜数D(N)不超过N/4*∏(p-2)/p*∏(p-1)/(p-2)*1/1.2609，式中第一个连乘积中的p取尽N平方根内所有奇素数，第二个连乘积中的p仅取能够整除N且不超过N平方根的奇素数；
或大偶数N的单计哥猜数D(N)不超过N/4p*∏c/(c-2)*∏(p-1)/(p-2)*1/1.2609，式中第一因子N/4p分母中的p是N平方根内最大奇素数，第一个连乘积∏c/(c-2)中的c是奇素数p前的最大奇合数，第二个连乘积中的p仅取能够整除N且不超过N平方根的奇素数；
或大偶数N的单计哥猜数D(N)不超过N/[2*p*(p-1)]*∏d/(d-2)*∏(p-1)/(p-2)*1/1.2609，式中第一因子N/[2*p*(p-1)]分母中的p是N平方根内最大奇素数，第一个连乘积∏d/(d-2)中的d是奇素数p前的最大偶合数(d=p-1)，第二个连乘积中的p仅取能够整除N且不超过N平方根的奇素数；

再简单一点的哥猜素数对下限公式是（略去大于等于1的波动因子∏(p-1)/(p-2)）
大偶数N的单计哥猜数D(N)不超过N/4*∏(p-2)/p*1/1.2609，式中连乘积∏(p-2)/p中的p取尽N平方根内所有奇素数；
或大偶数N的单计哥猜数D(N)不超过√N/4*∏c/(c-2)*1/1.2609，式中连乘积∏c/(c-2)中的c是奇素数p前的最大奇合数；
或大偶数N的单计哥猜数D(N)不超过1/2.5218*∏d/(d-2)，式中连乘积∏d/(d-2)中的d是奇素数p前的最大偶合数(d=p-1)。

4/9= 0.444444444
1/2.5218= 0.393421984

yangchuanju · 发表于 2026-8-12 16:19

更精确一些的欧拉常数是——γ=0.577215664901532860606512090082402431042...
梅滕斯常数是——e^γ=1.7810724179901979852365041031071795491696452143034302053...
e^(-γ)=0.56145948356688516982414321479088078676571038692515316817233747964…
2*e^(-γ)=1.12291896713377033964828642958176157353142077385030633634467495928…
[2*e^(-γ)]^2=1.2609470067487735922440803854217578087091741574254646832292874641…
1/[2*e^(-γ)]^2=0.793054739531362631931978352267368744280739434443075114577341021047227…

yangchuanju · 发表于 2026-8-12 17:20

本帖最后由 yangchuanju 于 2026-8-12 17:35 编辑

由连乘积哥猜数约等于哈李对数计算式哥猜数的1.260947倍，估算10^17--10^308次方的连乘积——
（10^1--10^16连乘积是实际值）
连乘积哥数=偶数/4*连乘积*波因
连乘积=连乘积哥数*4/偶数/波因

10^n 根内最大素数素数连乘积连乘积倒数奇合数连乘积合数连乘积
10 3 0.33333333 3.00 1.00 1.00
100 7 0.14285714 7.00 1.00 3.00
1000 31 0.06209152 16.11 1.92 28.87
10000 97 0.03829704 26.11 3.71 178.31
100000 313 0.02461160 40.63 7.70 1201.74
1000000 997 0.01731263 57.76 17.26 8595.83
10000000 3137 0.01279268 78.17 40.13 62924.86
100000000 9973 0.00978883 102.16 97.62 486753.39
1000000000 31607 0.00774780 129.07 244.88 3869912.48
10000000000 99991 0.00627642 159.33 627.59 31376135.48
1E+11 316223 0.00518937 192.70 1641.00 259460084.5
1E+12 999983 0.00436093 229.31 4360.86 2180390944
1E+13 3162277 0.00371592 269.11 11750.78 18579600553
1E+14 9999991 0.00320414 312.10 32041.37 1.60207E+11
1E+15 31622743 0.00279115 358.27 88263.97 1.39557E+12
1E+16 99999989 0.00245320 407.63 245319.65 1.2266E+13
1E+17 316227731 0.00217309 460.17 687191.7813 1.08655E+14
1E+18 999999937 0.00193834 515.90 1938343.803 9.69172E+14
1E+19 3162277633 0.00173968 574.82 5501341.969 8.69839E+15
1E+20 9999999967 0.00157006 636.92 15700585.74 7.85029E+16
1E+21 31622776589 0.00142409 702.20 45033661.39 7.12045E+17
1E+22 99999999977 0.00129757 770.67 129756907.3 6.48785E+18
1E+23 3.162278E+11 0.00118719 842.33 3.754224E+08 5.935949E+19
1E+24 1.000000E+12 0.00109032 917.16 1.090318E+09 5.451592E+20
1E+25 3.162278E+12 0.00100484 995.19 3.177575E+09 5.024187E+21
1E+26 1.000000E+13 0.00092903 1076.39 9.290287E+09 4.645144E+22
1E+27 3.162278E+13 0.00086149 1160.78 2.724259E+10 4.307431E+23
1E+28 1.000000E+14 0.00080105 1248.36 8.010503E+10 4.005251E+24
1E+29 3.162278E+14 0.00074676 1339.12 2.361456E+11 3.733790E+25
1E+30 1.000000E+15 0.00069780 1433.07 6.978038E+11 3.489019E+26
1E+31 3.162278E+15 0.00065351 1530.20 2.066581E+12 3.267552E+27
1E+32 1.000000E+16 0.00061330 1630.51 6.133041E+12 3.066521E+28
1E+33 3.162278E+16 0.00057670 1734.01 1.823677E+13 2.883487E+29
1E+34 1.000000E+17 0.00054327 1840.70 5.432729E+13 2.716364E+30
1E+35 3.162278E+17 0.00051267 1950.56 1.621212E+14 2.563361E+31
1E+36 1.000000E+18 0.00048459 2063.62 4.845860E+14 2.422930E+32
1E+37 3.162278E+18 0.00045875 2179.85 1.450683E+15 2.293731E+33
1E+38 1.000000E+19 0.00043492 2299.28 4.349193E+15 2.174596E+34
1E+39 3.162278E+19 0.00041290 2421.88 1.305710E+16 2.064508E+35
1E+40 1.000000E+20 0.00039251 2547.68 3.925146E+16 1.962573E+36
1E+41 3.162278E+20 0.00037360 2676.65 1.181430E+17 1.868005E+37
1E+42 1.000000E+21 0.00035602 2808.81 3.560224E+17 1.780112E+38
1E+43 3.162278E+21 0.00033966 2944.16 1.074086E+18 1.698279E+39
1E+44 1.000000E+22 0.00032439 3082.69 3.243923E+18 1.621961E+40
1E+45 3.162278E+22 0.00031014 3224.40 9.807331E+18 1.550675E+41
1E+46 1.000000E+23 0.00029680 3369.30 2.967975E+19 1.483987E+42
1E+47 3.162278E+23 0.00028430 3517.38 8.990423E+19 1.421511E+43
1E+48 1.000000E+24 0.00027258 3668.65 2.725796E+20 1.362898E+44
1E+49 3.162278E+24 0.00026157 3823.11 8.271489E+20 1.307837E+45
1E+50 1.000000E+25 0.00025121 3980.74 2.512094E+21 1.256047E+46
1E+51 3.162278E+25 0.00024145 4141.57 7.635465E+21 1.207273E+47
1E+52 1.000000E+26 0.00023226 4305.57 2.322572E+22 1.161286E+48
1E+53 3.162278E+26 0.00022358 4472.76 7.070076E+22 1.117877E+49
1E+54 1.000000E+27 0.00021537 4643.14 2.153715E+23 1.076858E+50
1E+55 3.162278E+27 0.00020761 4816.70 6.565238E+23 1.038055E+51
1E+56 1.000000E+28 0.00020026 4993.44 2.002626E+24 1.001313E+52
1E+57 3.162278E+28 0.00019330 5173.37 6.112602E+24 9.664873E+52
1E+58 1.000000E+29 0.00018669 5356.49 1.866895E+25 9.334474E+53
1E+59 3.162278E+29 0.00018041 5542.79 5.705212E+25 9.020733E+54
1E+60 1.000000E+30 0.00017445 5732.27 1.744510E+26 8.722548E+55
1E+61 3.162278E+30 0.00016878 5924.94 5.337233E+26 8.438907E+56
1E+62 1.000000E+31 0.00016338 6120.79 1.633776E+27 8.168879E+57
1E+63 3.162278E+31 0.00015823 6319.83 5.003740E+27 7.911608E+58
1E+64 1.000000E+32 0.00015333 6522.05 1.533260E+28 7.666302E+59
1E+65 3.162278E+32 0.00014864 6727.46 4.700555E+28 7.432230E+60
1E+66 1.000000E+33 0.00014417 6936.05 1.441743E+29 7.208717E+61
1E+67 3.162278E+33 0.00013990 7147.82 4.424113E+29 6.995137E+62
1E+68 1.000000E+34 0.00013582 7362.78 1.358182E+30 6.790911E+63
1E+69 3.162278E+34 0.00013191 7580.93 4.171360E+30 6.595499E+64
1E+70 1.000000E+35 0.00012817 7802.26 1.281680E+31 6.408402E+65
1E+71 3.162278E+35 0.00012458 8026.77 3.939664E+31 6.229155E+66
1E+72 1.000000E+36 0.00012115 8254.47 1.211465E+32 6.057325E+67
1E+73 3.162278E+36 0.00011785 8485.35 3.726749E+32 5.892507E+68
1E+74 1.000000E+37 0.00011469 8719.42 1.146865E+33 5.734326E+69
1E+75 3.162278E+37 0.00011165 8956.67 3.530639E+33 5.582431E+70
1E+76 1.000000E+38 0.00010873 9197.11 1.087298E+34 5.436491E+71
1E+77 3.162278E+38 0.00010592 9440.73 3.349611E+34 5.296200E+72
1E+78 1.000000E+39 0.00010323 9687.54 1.032254E+35 5.161271E+73
1E+79 3.162278E+39 0.00010063 9937.53 3.182157E+35 5.031433E+74
1E+80 1.000000E+40 0.00009813 10190.70 9.812866E+35 4.906433E+75
1E+81 3.162278E+40 0.00009572 10447.06 3.026954E+36 4.786034E+76
1E+82 1.000000E+41 0.00009340 10706.61 9.340027E+36 4.670014E+77
1E+83 3.162278E+41 0.00009116 10969.34 2.882834E+37 4.558161E+78
1E+84 1.000000E+42 0.00008901 11235.25 8.900559E+37 4.450279E+79
1E+85 3.162278E+42 0.00008692 11504.35 2.748767E+38 4.346183E+80
1E+86 1.000000E+43 0.00008491 11776.63 8.491393E+38 4.245697E+81
1E+87 3.162278E+43 0.00008297 12052.10 2.623840E+39 4.148655E+82
1E+88 1.000000E+44 0.00008110 12330.75 8.109807E+39 4.054903E+83
1E+89 3.162278E+44 0.00007929 12612.59 2.507240E+40 3.964294E+84
1E+90 1.000000E+45 0.00007753 12897.61 7.753376E+40 3.876688E+85
1E+91 3.162278E+45 0.00007584 13185.81 2.398242E+41 3.791954E+86
1E+92 1.000000E+46 0.00007420 13477.20 7.419937E+41 3.709968E+87
1E+93 3.162278E+46 0.00007261 13771.78 2.296201E+42 3.630613E+88
1E+94 1.000000E+47 0.00007108 14069.54 7.107554E+42 3.553777E+89
1E+95 3.162278E+47 0.00006959 14370.48 2.200537E+43 3.479354E+90
1E+96 1.000000E+48 0.00006814 14674.61 6.814490E+43 3.407245E+91
1E+97 3.162278E+48 0.00006675 14981.93 2.110729E+44 3.337355E+92
1E+98 1.000000E+49 0.00006539 15292.42 6.539186E+44 3.269593E+93
1E+99 3.162278E+49 0.00006408 15606.11 2.026308E+45 3.203874E+94
1E+100 1.000000E+50 0.00006280 15922.97 6.280234E+45 3.140117E+95
1E+101 3.162278E+50 0.00006156 16243.02 1.946853E+46 3.078244E+96
1E+102 1.000000E+51 0.00006036 16566.26 6.036365E+46 3.018183E+97
1E+103 3.162278E+51 0.00005920 16892.68 1.871981E+47 2.959862E+98
1E+104 1.000000E+52 0.00005806 17222.29 5.806430E+47 2.903215E+99
1E+105 3.162278E+52 0.00005696 17555.08 1.801346E+48 2.848179E+100
1E+106 1.000000E+53 0.00005589 17891.05 5.589386E+48 2.794693E+101
1E+107 3.162278E+53 0.00005485 18230.21 1.734636E+49 2.742700E+102
1E+108 1.000000E+54 0.00005384 18572.56 5.384289E+49 2.692144E+103
1E+109 3.162278E+54 0.00005286 18918.08 1.671563E+50 2.642974E+104
1E+110 1.000000E+55 0.00005190 19266.80 5.190276E+50 2.595138E+105
1E+111 3.162278E+55 0.00005097 19618.69 1.611870E+51 2.548590E+106
1E+112 1.000000E+56 0.00005007 19973.78 5.006564E+51 2.503282E+107
1E+113 3.162278E+56 0.00004918 20332.04 1.555317E+52 2.459172E+108
1E+114 1.000000E+57 0.00004832 20693.50 4.832436E+52 2.416218E+109
1E+115 3.162278E+57 0.00004749 21058.13 1.501690E+53 2.374380E+110
1E+116 1.000000E+58 0.00004667 21425.95 4.667237E+53 2.333619E+111
1E+117 3.162278E+58 0.00004588 21796.96 1.450789E+54 2.293898E+112
1E+118 1.000000E+59 0.00004510 22171.15 4.510367E+54 2.255183E+113
1E+119 3.162278E+59 0.00004435 22548.52 1.402432E+55 2.217440E+114
1E+120 1.000000E+60 0.00004361 22929.08 4.361274E+55 2.180637E+115
1E+121 3.162278E+60 0.00004289 23312.82 1.356454E+56 2.144742E+116
1E+122 1.000000E+61 0.00004219 23699.75 4.219453E+56 2.109727E+117
1E+123 3.162278E+61 0.00004151 24089.87 1.312700E+57 2.075562E+118
1E+124 1.000000E+62 0.00004084 24483.16 4.084440E+57 2.042220E+119
1E+125 3.162278E+62 0.00004019 24879.64 1.271030E+58 2.009675E+120
1E+126 1.000000E+63 0.00003956 25279.31 3.955804E+58 1.977902E+121
1E+127 3.162278E+63 0.00003894 25682.16 1.231313E+59 1.946877E+122
1E+128 1.000000E+64 0.00003833 26088.20 3.833151E+59 1.916575E+123
1E+129 3.162278E+64 0.00003774 26497.42 1.193429E+60 1.886976E+124
1E+130 1.000000E+65 0.00003716 26909.82 3.716115E+60 1.858057E+125
1E+131 3.162278E+65 0.00003660 27325.41 1.157266E+61 1.829798E+126
1E+132 1.000000E+66 0.00003604 27744.19 3.604359E+61 1.802179E+127
1E+133 3.162278E+66 0.00003550 28166.15 1.122723E+62 1.775181E+128
1E+134 1.000000E+67 0.00003498 28591.29 3.497569E+62 1.748784E+129
1E+135 3.162278E+67 0.00003446 29019.62 1.089703E+63 1.722972E+130
1E+136 1.000000E+68 0.00003395 29451.13 3.395455E+63 1.697728E+131
1E+137 3.162278E+68 0.00003346 29885.83 1.058119E+64 1.673034E+132
1E+138 1.000000E+69 0.00003298 30323.71 3.297750E+64 1.648875E+133
1E+139 3.162278E+69 0.00003250 30764.78 1.027889E+65 1.625235E+134
1E+140 1.000000E+70 0.00003204 31209.03 3.204201E+65 1.602101E+135
1E+141 3.162278E+70 0.00003159 31656.46 9.989359E+65 1.579456E+136
1E+142 1.000000E+71 0.00003115 32107.08 3.114578E+66 1.557289E+137
1E+143 3.162278E+71 0.00003071 32560.89 9.711890E+66 1.535585E+138
1E+144 1.000000E+72 0.00003029 33017.88 3.028662E+67 1.514331E+139
1E+145 3.162278E+72 0.00002987 33478.05 9.445824E+67 1.493516E+140
1E+146 1.000000E+73 0.00002946 33941.41 2.946254E+68 1.473127E+141
1E+147 3.162278E+73 0.00002906 34407.95 9.190543E+68 1.453152E+142
1E+148 1.000000E+74 0.00002867 34877.68 2.867163E+69 1.433582E+143
1E+149 3.162278E+74 0.00002829 35350.59 8.945473E+69 1.414403E+144
1E+150 1.000000E+75 0.00002791 35826.69 2.791215E+70 1.395608E+145

yangchuanju · 发表于 2026-8-12 17:25

本帖最后由 yangchuanju 于 2026-8-12 17:27 编辑

（接上楼）
10^n 根内最大素数素数连乘积连乘积倒数奇合数连乘积合数连乘积
1E+151 3.162278E+75 0.00002754 36305.97 8.710076E+70 1.377184E+146
1E+152 1.000000E+76 0.00002718 36788.44 2.718245E+71 1.359123E+147
1E+153 3.162278E+76 0.00002683 37274.09 8.483850E+71 1.341414E+148
1E+154 1.000000E+77 0.00002648 37762.92 2.648100E+72 1.324050E+149
1E+155 3.162278E+77 0.00002614 38254.94 8.266325E+72 1.307021E+150
1E+156 1.000000E+78 0.00002581 38750.15 2.580635E+73 1.290318E+151
1E+157 3.162278E+78 0.00002548 39248.54 8.057059E+73 1.273933E+152
1E+158 1.000000E+79 0.00002516 39750.11 2.515716E+74 1.257858E+153
1E+159 3.162278E+79 0.00002484 40254.87 7.855640E+74 1.242086E+154
1E+160 1.000000E+80 0.00002453 40762.81 2.453217E+75 1.226608E+155
1E+161 3.162278E+80 0.00002423 41273.94 7.661682E+75 1.211418E+156
1E+162 1.000000E+81 0.00002393 41788.25 2.393017E+76 1.196509E+157
1E+163 3.162278E+81 0.00002364 42305.75 7.474818E+76 1.181873E+158
1E+164 1.000000E+82 0.00002335 42826.43 2.335007E+77 1.167503E+159
1E+165 3.162278E+82 0.00002307 43350.29 7.294709E+77 1.153395E+160
1E+166 1.000000E+83 0.00002279 43877.34 2.279081E+78 1.139540E+161
1E+167 3.162278E+83 0.00002252 44407.58 7.121031E+78 1.125934E+162
1E+168 1.000000E+84 0.00002225 44941.00 2.225140E+79 1.112570E+163
1E+169 3.162278E+84 0.00002199 45477.60 6.953484E+79 1.099442E+164
1E+170 1.000000E+85 0.00002173 46017.39 2.173091E+80 1.086546E+165
1E+171 3.162278E+85 0.00002148 46560.36 6.791780E+80 1.073875E+166
1E+172 1.000000E+86 0.00002123 47106.52 2.122848E+81 1.061424E+167
1E+173 3.162278E+86 0.00002098 47655.87 6.635653E+81 1.049189E+168
1E+174 1.000000E+87 0.00002074 48208.39 2.074328E+82 1.037164E+169
1E+175 3.162278E+87 0.00002051 48764.10 6.484847E+82 1.025344E+170
1E+176 1.000000E+88 0.00002027 49323.00 2.027452E+83 1.013726E+171
1E+177 3.162278E+88 0.00002005 49885.08 6.339125E+83 1.002304E+172
1E+178 1.000000E+89 0.00001982 50450.35 1.982147E+84 9.910735E+172
1E+179 3.162278E+89 0.00001960 51018.80 6.198260E+84 9.800309E+173
1E+180 1.000000E+90 0.00001938 51590.43 1.938344E+85 9.691720E+174
1E+181 3.162278E+90 0.00001917 52165.25 6.062039E+85 9.584925E+175
1E+182 1.000000E+91 0.00001896 52743.25 1.895977E+86 9.479885E+176
1E+183 3.162278E+91 0.00001875 53324.44 5.930259E+86 9.376563E+177
1E+184 1.000000E+92 0.00001855 53908.82 1.854984E+87 9.274921E+178
1E+185 3.162278E+92 0.00001835 54496.37 5.802730E+87 9.174922E+179
1E+186 1.000000E+93 0.00001815 55087.12 1.815306E+88 9.076532E+180
1E+187 3.162278E+93 0.00001796 55681.04 5.679272E+88 8.979717E+181
1E+188 1.000000E+94 0.00001777 56278.15 1.776888E+89 8.884442E+182
1E+189 3.162278E+94 0.00001758 56878.45 5.559711E+89 8.790675E+183
1E+190 1.000000E+95 0.00001740 57481.93 1.739677E+90 8.698385E+184
1E+191 3.162278E+95 0.00001722 58088.60 5.443887E+90 8.607541E+185
1E+192 1.000000E+96 0.00001704 58698.45 1.703623E+91 8.518113E+186
1E+193 3.162278E+96 0.00001686 59311.48 5.331645E+91 8.430071E+187
1E+194 1.000000E+97 0.00001669 59927.70 1.668677E+92 8.343387E+188
1E+195 3.162278E+97 0.00001652 60547.10 5.222839E+92 8.258033E+189
1E+196 1.000000E+98 0.00001635 61169.69 1.634797E+93 8.173983E+190
1E+197 3.162278E+98 0.00001618 61795.47 5.117330E+93 8.091209E+191
1E+198 1.000000E+99 0.00001602 62424.42 1.601937E+94 8.009686E+192
1E+199 3.162278E+99 0.00001586 63056.56 5.014986E+94 7.929389E+193
1E+200 1.000000E+100 0.00001570 63691.89 1.570059E+95 7.850293E+194
1E+201 3.162278E+100 0.00001554 64330.40 4.915681E+95 7.772375E+195
1E+202 1.000000E+101 0.00001539 64972.10 1.539122E+96 7.695611E+196
1E+203 3.162278E+101 0.00001524 65616.98 4.819298E+96 7.619979E+197
1E+204 1.000000E+102 0.00001509 66265.04 1.509091E+97 7.545456E+198
1E+205 3.162278E+102 0.00001494 66916.29 4.725722E+97 7.472022E+199
1E+206 1.000000E+103 0.00001480 67570.73 1.479931E+98 7.399654E+200
1E+207 3.162278E+103 0.00001466 68228.35 4.634844E+98 7.328332E+201
1E+208 1.000000E+104 0.00001452 68889.15 1.451607E+99 7.258037E+202
1E+209 3.162278E+104 0.00001438 69553.14 4.546564E+99 7.188748E+203
1E+210 1.000000E+105 0.00001424 70220.31 1.424089E+100 7.120447E+204
1E+211 3.162278E+105 0.00001411 70890.67 4.460781E+100 7.053115E+205
1E+212 1.000000E+106 0.00001397 71564.21 1.397347E+101 6.986733E+206
1E+213 3.162278E+106 0.00001384 72240.94 4.377404E+101 6.921284E+207
1E+214 1.000000E+107 0.00001371 72920.85 1.371350E+102 6.856750E+208
1E+215 3.162278E+107 0.00001359 73603.94 4.296343E+102 6.793114E+209
1E+216 1.000000E+108 0.00001346 74290.22 1.346072E+103 6.730361E+210
1E+217 3.162278E+108 0.00001334 74979.69 4.217513E+103 6.668473E+211
1E+218 1.000000E+109 0.00001321 75672.34 1.321487E+104 6.607434E+212
1E+219 3.162278E+109 0.00001309 76368.17 4.140832E+104 6.547230E+213
1E+220 1.000000E+110 0.00001298 77067.19 1.297569E+105 6.487845E+214
1E+221 3.162278E+110 0.00001286 77769.39 4.066224E+105 6.429265E+215
1E+222 1.000000E+111 0.00001274 78474.78 1.274295E+106 6.371474E+216
1E+223 3.162278E+111 0.00001263 79183.35 3.993614E+106 6.314459E+217
1E+224 1.000000E+112 0.00001252 79895.11 1.251641E+107 6.258205E+218
1E+225 3.162278E+112 0.00001241 80610.05 3.922932E+107 6.202701E+219
1E+226 1.000000E+113 0.00001230 81328.18 1.229586E+108 6.147931E+220
1E+227 3.162278E+113 0.00001219 82049.49 3.854110E+108 6.093883E+221
1E+228 1.000000E+114 0.00001208 82773.98 1.208109E+109 6.040545E+222
1E+229 3.162278E+114 0.00001198 83501.66 3.787084E+109 5.987905E+223
1E+230 1.000000E+115 0.00001187 84232.53 1.187190E+110 5.935949E+224
1E+231 3.162278E+115 0.00001177 84966.57 3.721790E+110 5.884667E+225
1E+232 1.000000E+116 0.00001167 85703.81 1.166809E+111 5.834046E+226
1E+233 3.162278E+116 0.00001157 86444.23 3.658171E+111 5.784076E+227
1E+234 1.000000E+117 0.00001147 87187.83 1.146949E+112 5.734745E+228
1E+235 3.162278E+117 0.00001137 87934.62 3.596169E+112 5.686043E+229
1E+236 1.000000E+118 0.00001128 88684.59 1.127592E+113 5.637958E+230
1E+237 3.162278E+118 0.00001118 89437.75 3.535731E+113 5.590481E+231
1E+238 1.000000E+119 0.00001109 90194.09 1.108720E+114 5.543601E+232
1E+239 3.162278E+119 0.00001099 90953.61 3.476803E+114 5.497308E+233
1E+240 1.000000E+120 0.00001090 91716.32 1.090318E+115 5.451592E+234
1E+241 3.162278E+120 0.00001081 92482.22 3.419336E+115 5.406445E+235
1E+242 1.000000E+121 0.00001072 93251.30 1.072371E+116 5.361856E+236
1E+243 3.162278E+121 0.00001064 94023.56 3.363282E+116 5.317816E+237
1E+244 1.000000E+122 0.00001055 94799.01 1.054863E+117 5.274317E+238
1E+245 3.162278E+122 0.00001046 95577.64 3.308596E+117 5.231349E+239
1E+246 1.000000E+123 0.00001038 96359.46 1.037781E+118 5.188904E+240
1E+247 3.162278E+123 0.00001029 97144.46 3.255232E+118 5.146974E+241
1E+248 1.000000E+124 0.00001021 97932.65 1.021110E+119 5.105549E+242
1E+249 3.162278E+124 0.00001013 98724.02 3.203149E+119 5.064623E+243
1E+250 1.000000E+125 0.00001005 99518.58 1.004837E+120 5.024187E+244
1E+251 3.162278E+125 0.00000997 100316.32 3.152306E+120 4.984234E+245
1E+252 1.000000E+126 0.00000989 101117.25 9.889510E+120 4.944755E+246
1E+253 3.162278E+126 0.00000981 101921.36 3.102664E+121 4.905743E+247
1E+254 1.000000E+127 0.00000973 102728.65 9.734383E+121 4.867191E+248
1E+255 3.162278E+127 0.00000966 103539.13 3.054186E+122 4.829092E+249
1E+256 1.000000E+128 0.00000958 104352.79 9.582877E+122 4.791439E+250
1E+257 3.162278E+128 0.00000951 105169.64 3.006835E+123 4.754224E+251
1E+258 1.000000E+129 0.00000943 105989.68 9.434881E+123 4.717441E+252
1E+259 3.162278E+129 0.00000936 106812.89 2.960577E+124 4.681083E+253
1E+260 1.000000E+130 0.00000929 107639.30 9.290287E+124 4.645144E+254
1E+261 3.162278E+130 0.00000922 108468.88 2.915378E+125 4.609617E+255
1E+262 1.000000E+131 0.00000915 109301.65 9.148992E+125 4.574496E+256
1E+263 3.162278E+131 0.00000908 110137.61 2.871206E+126 4.539775E+257
1E+264 1.000000E+132 0.00000901 110976.75 9.010896E+126 4.505448E+258
1E+265 3.162278E+132 0.00000894 111819.08 2.828031E+127 4.471509E+259
1E+266 1.000000E+133 0.00000888 112664.59 8.875904E+127 4.437952E+260
1E+267 3.162278E+133 0.00000881 113513.28 2.785822E+128 4.404771E+261
1E+268 1.000000E+134 0.00000874 114365.16 8.743922E+128 4.371961E+262
1E+269 3.162278E+134 0.00000868 115220.22 2.744551E+129 4.339516E+263
1E+270 1.000000E+135 0.00000861 116078.47 8.614862E+129 4.307431E+264
1E+271 3.162278E+135 0.00000855 116939.90 2.704190E+130 4.275700E+265
1E+272 1.000000E+136 0.00000849 117804.52 8.488639E+130 4.244319E+266
1E+273 3.162278E+136 0.00000843 118672.32 2.664714E+131 4.213282E+267
1E+274 1.000000E+137 0.00000837 119543.31 8.365169E+131 4.182585E+268
1E+275 3.162278E+137 0.00000830 120417.48 2.626095E+132 4.152221E+269
1E+276 1.000000E+138 0.00000824 121294.84 8.244374E+132 4.122187E+270
1E+277 3.162278E+138 0.00000818 122175.38 2.588310E+133 4.092478E+271
1E+278 1.000000E+139 0.00000813 123059.10 8.126177E+133 4.063088E+272
1E+279 3.162278E+139 0.00000807 123946.01 2.551335E+134 4.034014E+273
1E+280 1.000000E+140 0.00000801 124836.11 8.010503E+134 4.005251E+274
1E+281 3.162278E+140 0.00000795 125729.39 2.515146E+135 3.976795E+275
1E+282 1.000000E+141 0.00000790 126625.85 7.897282E+135 3.948641E+276
1E+283 3.162278E+141 0.00000784 127525.50 2.479722E+136 3.920785E+277
1E+284 1.000000E+142 0.00000779 128428.33 7.786444E+136 3.893222E+278
1E+285 3.162278E+142 0.00000773 129334.35 2.445041E+137 3.865949E+279
1E+286 1.000000E+143 0.00000768 130243.55 7.677924E+137 3.838962E+280
1E+287 3.162278E+143 0.00000762 131155.93 2.411082E+138 3.812256E+281
1E+288 1.000000E+144 0.00000757 132071.51 7.571656E+138 3.785828E+282
1E+289 3.162278E+144 0.00000752 132990.26 2.377826E+139 3.759674E+283
1E+290 1.000000E+145 0.00000747 133912.20 7.467579E+139 3.733790E+284
1E+291 3.162278E+145 0.00000742 134837.33 2.345254E+140 3.708172E+285
1E+292 1.000000E+146 0.00000737 135765.64 7.365634E+140 3.682817E+286
1E+293 3.162278E+146 0.00000732 136697.13 2.313346E+141 3.657721E+287
1E+294 1.000000E+147 0.00000727 137631.81 7.265762E+141 3.632881E+288
1E+295 3.162278E+147 0.00000722 138569.67 2.282085E+142 3.608293E+289
1E+296 1.000000E+148 0.00000717 139510.72 7.167908E+142 3.583954E+290
1E+297 3.162278E+148 0.00000712 140454.95 2.251453E+143 3.559860E+291
1E+298 1.000000E+149 0.00000707 141402.37 7.072017E+143 3.536009E+292
1E+299 3.162278E+149 0.00000702 142352.97 2.221434E+144 3.512396E+293
1E+300 1.000000E+150 0.00000698 143306.75 6.978038E+144 3.489019E+294
1E+301 3.162278E+150 0.00000693 144263.73 2.192012E+145 3.465875E+295
1E+302 1.000000E+151 0.00000689 145223.88 6.885920E+145 3.442960E+296
1E+303 3.162278E+151 0.00000684 146187.22 2.163170E+146 3.420272E+297
1E+304 1.000000E+152 0.00000680 147153.75 6.795614E+146 3.397807E+298
1E+305 3.162278E+152 0.00000675 148123.45 2.134893E+147 3.375563E+299
1E+306 1.000000E+153 0.00000671 149096.35 6.707072E+147 3.353536E+300
1E+307 3.162278E+153 0.00000666 150072.43 2.107168E+148 3.331725E+301
1E+308 1.000000E+154 0.00000662 151051.69 6.620250E+148 3.310125E+302

yangchuanju · 发表于 2026-8-13 04:03

本帖最后由 yangchuanju 于 2026-8-13 04:07 编辑

连乘积哥猜数一般大于真实哥猜数，哈李对数计算式哥猜数一般小于真实哥猜数，因而连乘积哥猜数一般是大于哈李哥猜数的（290以上偶数都大了）；
连乘积哥猜数与哈李哥猜数之比呈不规则锯齿状变化，升降升降……，并逐渐趋近于1.26047；
真实哥猜数介于两个伪哥猜数之间，当偶数较大时与哈李哥猜数较近些；
当偶数趋近于无穷大时，偶数的真实哥猜数趋近于按哈李对数计算式计算的哈李哥猜数。

素数小偶数小偶连乘哥数/哈李哥数大偶数大偶连乘哥数/哈李哥数
3 10 0.669267 24 1.274943
5 26 0.803984 48 1.135040
7 50 0.827931 120 1.239960
11 122 1.021530 168 1.162127
13 170 0.987886 288 1.201096
17 290 1.062383 360 1.144956
19 362 1.026364 528 1.162086
23 530 1.062315 840 1.224021
29 842 1.140411 960 1.185254
31 962 1.109458 1368 1.226109
37 1370 1.160303 1680 1.226768
41 1682 1.167299 1848 1.197070
43 1850 1.141720 2208 1.196046
47 2210 1.145420 2808 1.217769
53 2810 1.172026 3480 1.236001
59 3482 1.194270 3720 1.213713
61 3722 1.174073 4488 1.228129
67 4490 1.191594 5040 1.224566
71 5042 1.190182 5328 1.205636
73 5330 1.172708 6240 1.216187
79 6242 1.185484 6888 1.212353
83 6890 1.183218 7920 1.220816
89 7922 1.193449 9408 1.239596
97 9410 1.214094 10200 1.235582
101 10202 1.211167 10608 1.221430
103 10610 1.197761 11448 1.217487
107 11450 1.194775 11880 1.204220
109 11882 1.182167 12768 1.200358
113 12770 1.179152 16128 1.238102
127 16130 1.218635 17160 1.234257
131 17162 1.215443 19320 1.245151
139 19322 1.226999 22200 1.261768

风花飘飘 · 发表于 2026-8-13 04:09

wangyangke 发表于 2026-8-11 06:28
实话实说：yangchuanju蹦蹦跳跳，其在哥德巴赫猜想方面，与鲁思顺不相上下或者相当。

你就是根搅屎棍子！
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