基础理论中的两个重要定理的证明

ysr · 发表于 2026-4-1 13:43

在10000内的这样的素数组有108 组：
(5 17 23 )
(11 23 29 )
(19 31 37 )
(29 41 47 )
(41 53 59 )
(61 73 79 )
(71 83 89 )
(89 101 107 )
(139 151 157 )
(179 191 197 )
(181 193 199 )
(211 223 229 )
(239 251 257 )
(251 263 269 )
(421 433 439 )
(431 443 449 )
(449 461 467 )
(491 503 509 )
(601 613 619 )
(641 653 659 )
(739 751 757 )
(809 821 827 )
(811 823 829 )
(929 941 947 )
(1021 1033 1039 )
(1051 1063 1069 )
(1091 1103 1109 )
(1279 1291 1297 )
(1289 1301 1307 )
(1471 1483 1489 )
(1481 1493 1499 )
(1531 1543 1549 )
(1601 1613 1619 )
(1609 1621 1627 )
(1741 1753 1759 )
(1861 1873 1879 )
(1889 1901 1907 )
(1999 2011 2017 )
(2069 2081 2087 )
(2269 2281 2287 )
(2339 2351 2357 )
(2371 2383 2389 )
(2381 2393 2399 )
(2399 2411 2417 )
(2531 2543 2549 )
(2539 2551 2557 )
(2659 2671 2677 )
(2671 2683 2689 )
(3049 3061 3067 )
(3169 3181 3187 )
(3191 3203 3209 )
(3301 3313 3319 )
(3449 3461 3467 )
(3499 3511 3517 )
(3529 3541 3547 )
(3659 3671 3677 )
(3911 3923 3929 )
(3989 4001 4007 )
(4001 4013 4019 )
(4241 4253 4259 )
(4271 4283 4289 )
(4549 4561 4567 )
(4639 4651 4657 )
(4919 4931 4937 )
(5101 5113 5119 )
(5261 5273 5279 )
(5381 5393 5399 )
(5419 5431 5437 )
(5431 5443 5449 )
(5639 5651 5657 )
(5641 5653 5659 )
(5839 5851 5857 )
(5849 5861 5867 )
(6199 6211 6217 )
(6299 6311 6317 )
(6311 6323 6329 )
(6361 6373 6379 )
(6551 6563 6569 )
(6661 6673 6679 )
(6691 6703 6709 )
(6899 6911 6917 )
(6949 6961 6967 )
(6959 6971 6977 )
(7001 7013 7019 )
(7109 7121 7127 )
(7529 7541 7547 )
(7669 7681 7687 )
(7741 7753 7759 )
(8069 8081 8087 )
(8219 8231 8237 )
(8629 8641 8647 )
(8681 8693 8699 )
(8719 8731 8737 )
(8819 8831 8837 )
(8849 8861 8867 )
(8951 8963 8969 )
(9091 9103 9109 )
(9209 9221 9227 )
(9419 9431 9437 )
(9421 9433 9439 )
(9461 9473 9479 )
(9479 9491 9497 )
(9521 9533 9539 )
(9601 9613 9619 )
(9631 9643 9649 )
(9721 9733 9739 )
(9769 9781 9787 )
(9839 9851 9857 )
命题：项差依次为12，6的3生素数组有无穷多，其中有的组中间可能还有其他素数。

ysr · 发表于 2026-4-1 13:44

在10000内的这样的素数组有57 组：
(3 5 11 )
(5 7 13 )
(11 13 19 )
(29 31 37 )
(59 61 67 )
(71 73 79 )
(101 103 109 )
(149 151 157 )
(191 193 199 )
(269 271 277 )
(431 433 439 )
(569 571 577 )
(599 601 607 )
(821 823 829 )
(1031 1033 1039 )
(1061 1063 1069 )
(1229 1231 1237 )
(1289 1291 1297 )
(1319 1321 1327 )
(1451 1453 1459 )
(1481 1483 1489 )
(1619 1621 1627 )
(1871 1873 1879 )
(2081 2083 2089 )
(2129 2131 2137 )
(2339 2341 2347 )
(2381 2383 2389 )
(2549 2551 2557 )
(2711 2713 2719 )
(2789 2791 2797 )
(3251 3253 3259 )
(3299 3301 3307 )
(3461 3463 3469 )
(3539 3541 3547 )
(4019 4021 4027 )
(4049 4051 4057 )
(4091 4093 4099 )
(4649 4651 4657 )
(4721 4723 4729 )
(5099 5101 5107 )
(5441 5443 5449 )
(5519 5521 5527 )
(5639 5641 5647 )
(5651 5653 5659 )
(5741 5743 5749 )
(5849 5851 5857 )
(6269 6271 6277 )
(6359 6361 6367 )
(6569 6571 6577 )
(6701 6703 6709 )
(6959 6961 6967 )
(7211 7213 7219 )
(8009 8011 8017 )
(8999 9001 9007 )
(9041 9043 9049 )
(9341 9343 9349 )
(9431 9433 9439 )
命题：项差依次为2，6的3生素数组有无穷多，其中有的组中间可能还有其他素数。

ysr · 发表于 2026-4-1 13:46

在10000内的这样的素数组有115 组：
(3 17 23 )
(17 31 37 )
(23 37 43 )
(47 61 67 )
(53 67 73 )
(59 73 79 )
(83 97 103 )
(89 103 109 )
(137 151 157 )
(179 193 199 )
(257 271 277 )
(263 277 283 )
(293 307 313 )
(317 331 337 )
(353 367 373 )
(359 373 379 )
(419 433 439 )
(443 457 463 )
(557 571 577 )
(587 601 607 )
(593 607 613 )
(599 613 619 )
(719 733 739 )
(809 823 829 )
(839 853 859 )
(863 877 883 )
(977 991 997 )
(1019 1033 1039 )
(1049 1063 1069 )
(1103 1117 1123 )
(1109 1123 1129 )
(1217 1231 1237 )
(1277 1291 1297 )
(1283 1297 1303 )
(1307 1321 1327 )
(1409 1423 1429 )
(1433 1447 1453 )
(1439 1453 1459 )
(1607 1621 1627 )
(1733 1747 1753 )
(1847 1861 1867 )
(1973 1987 1993 )
(1979 1993 1999 )
(1997 2011 2017 )
(2069 2083 2089 )
(2267 2281 2287 )
(2273 2287 2293 )
(2357 2371 2377 )
(2657 2671 2677 )
(2663 2677 2683 )
(2693 2707 2713 )
(2699 2713 2719 )
(2777 2791 2797 )
(2837 2851 2857 )
(3167 3181 3187 )
(3299 3313 3319 )
(3449 3463 3469 )
(3527 3541 3547 )
(3593 3607 3613 )
(3617 3631 3637 )
(3623 3637 3643 )
(3677 3691 3697 )
(3719 3733 3739 )
(3833 3847 3853 )
(4007 4021 4027 )
(4079 4093 4099 )
(4139 4153 4159 )
(4493 4507 4513 )
(4547 4561 4567 )
(4583 4597 4603 )
(4637 4651 4657 )
(4643 4657 4663 )
(4889 4903 4909 )
(4937 4951 4957 )
(4973 4987 4993 )
(5087 5101 5107 )
(5099 5113 5119 )
(5393 5407 5413 )
(5399 5413 5419 )
(5417 5431 5437 )
(5507 5521 5527 )
(5639 5653 5659 )
(5669 5683 5689 )
(5807 5821 5827 )
(6053 6067 6073 )
(6197 6211 6217 )
(6257 6271 6277 )
(6323 6337 6343 )
(6353 6367 6373 )
(6359 6373 6379 )
(6659 6673 6679 )
(6689 6703 6709 )
(6947 6961 6967 )
(6977 6991 6997 )
(7193 7207 7213 )
(7703 7717 7723 )
(7853 7867 7873 )
(8039 8053 8059 )
(8147 8161 8167 )
(8273 8287 8293 )
(8297 8311 8317 )
(8447 8461 8467 )
(8609 8623 8629 )
(8627 8641 8647 )
(8693 8707 8713 )
(8699 8713 8719 )
(9029 9043 9049 )
(9137 9151 9157 )
(9323 9337 9343 )
(9377 9391 9397 )
(9419 9433 9439 )
(9629 9643 9649 )
(9719 9733 9739 )
(9767 9781 9787 )
(9887 9901 9907 )
命题：项差依次为14，6的3生素数组有无穷多，其中有的组中间可能还有其他素数。

ysr · 发表于 2026-4-1 13:47

在10000内的这样的素数组有68 组：
(7 23 29 )
(31 47 53 )
(37 53 59 )
(67 83 89 )
(151 167 173 )
(157 173 179 )
(211 227 233 )
(241 257 263 )
(331 347 353 )
(337 353 359 )
(367 383 389 )
(487 503 509 )
(541 557 563 )
(547 563 569 )
(571 587 593 )
(577 593 599 )
(631 647 653 )
(661 677 683 )
(997 1013 1019 )
(1087 1103 1109 )
(1171 1187 1193 )
(1201 1217 1223 )
(1471 1487 1493 )
(1597 1613 1619 )
(2221 2237 2243 )
(2251 2267 2273 )
(2377 2393 2399 )
(2671 2687 2693 )
(2677 2693 2699 )
(2887 2903 2909 )
(3067 3083 3089 )
(3187 3203 3209 )
(3307 3323 3329 )
(3391 3407 3413 )
(3511 3527 3533 )
(3517 3533 3539 )
(3907 3923 3929 )
(4057 4073 4079 )
(4111 4127 4133 )
(4441 4457 4463 )
(4621 4637 4643 )
(4657 4673 4679 )
(4951 4967 4973 )
(4987 5003 5009 )
(5281 5297 5303 )
(5791 5807 5813 )
(5827 5843 5849 )
(5881 5897 5903 )
(6247 6263 6269 )
(6301 6317 6323 )
(6337 6353 6359 )
(6547 6563 6569 )
(6637 6653 6659 )
(6841 6857 6863 )
(6961 6977 6983 )
(6997 7013 7019 )
(7507 7523 7529 )
(7561 7577 7583 )
(8101 8117 8123 )
(8221 8237 8243 )
(8521 8537 8543 )
(8647 8663 8669 )
(8677 8693 8699 )
(8731 8747 8753 )
(9187 9203 9209 )
(9397 9413 9419 )
(9817 9833 9839 )
(9907 9923 9929 )
命题：项差依次为16，6的3生素数组有无穷多，其中有的组中间可能还有其他素数。

ysr · 发表于 2026-4-1 13:49

在10000内的这样的素数组有120 组：
(5 23 29 )
(13 31 37 )
(19 37 43 )
(23 41 47 )
(29 47 53 )
(43 61 67 )
(79 97 103 )
(83 101 107 )
(89 107 113 )
(113 131 137 )
(139 157 163 )
(149 167 173 )
(173 191 197 )
(233 251 257 )
(239 257 263 )
(293 311 317 )
(313 331 337 )
(349 367 373 )
(439 457 463 )
(443 461 467 )
(523 541 547 )
(569 587 593 )
(659 677 683 )
(709 727 733 )
(733 751 757 )
(839 857 863 )
(859 877 883 )
(863 881 887 )
(929 947 953 )
(953 971 977 )
(1069 1087 1093 )
(1163 1181 1187 )
(1213 1231 1237 )
(1259 1277 1283 )
(1279 1297 1303 )
(1283 1301 1307 )
(1303 1321 1327 )
(1409 1427 1433 )
(1429 1447 1453 )
(1583 1601 1607 )
(1723 1741 1747 )
(1759 1777 1783 )
(1889 1907 1913 )
(1979 1997 2003 )
(1993 2011 2017 )
(2063 2081 2087 )
(2113 2131 2137 )
(2269 2287 2293 )
(2333 2351 2357 )
(2393 2411 2417 )
(2399 2417 2423 )
(2423 2441 2447 )
(2659 2677 2683 )
(2689 2707 2713 )
(2819 2837 2843 )
(2833 2851 2857 )
(2879 2897 2903 )
(2939 2957 2963 )
(3163 3181 3187 )
(3389 3407 3413 )
(3613 3631 3637 )
(3673 3691 3697 )
(3709 3727 3733 )
(3779 3797 3803 )
(3989 4007 4013 )
(4003 4021 4027 )
(4339 4357 4363 )
(4373 4391 4397 )
(4423 4441 4447 )
(4639 4657 4663 )
(4919 4937 4943 )
(4933 4951 4957 )
(4969 4987 4993 )
(5209 5227 5233 )
(5279 5297 5303 )
(5413 5431 5437 )
(5419 5437 5443 )
(5483 5501 5507 )
(5503 5521 5527 )
(5623 5641 5647 )
(5693 5711 5717 )
(5783 5801 5807 )
(5843 5861 5867 )
(5879 5897 5903 )
(6029 6047 6053 )
(6299 6317 6323 )
(6343 6361 6367 )
(6529 6547 6553 )
(6553 6571 6577 )
(6959 6977 6983 )
(7103 7121 7127 )
(7219 7237 7243 )
(7229 7247 7253 )
(7393 7411 7417 )
(7433 7451 7457 )
(7499 7517 7523 )
(7523 7541 7547 )
(7559 7577 7583 )
(7699 7717 7723 )
(7883 7901 7907 )
(7993 8011 8017 )
(8069 8087 8093 )
(8093 8111 8117 )
(8219 8237 8243 )
(8269 8287 8293 )
(8273 8291 8297 )
(8293 8311 8317 )
(8443 8461 8467 )
(8623 8641 8647 )
(8689 8707 8713 )
(8713 8731 8737 )
(9109 9127 9133 )
(9133 9151 9157 )
(9203 9221 9227 )
(9319 9337 9343 )
(9413 9431 9437 )
(9473 9491 9497 )
(9833 9851 9857 )
(9883 9901 9907 )
(9949 9967 9973 )
命题：项差依次为18，6的3生素数组有无穷多，其中有的组中间可能还有其他素数。

ysr · 发表于 2026-4-1 13:50

在10000内的这样的素数组有94 组：
(3 23 29 )
(11 31 37 )
(17 37 43 )
(41 61 67 )
(47 67 73 )
(53 73 79 )
(83 103 109 )
(131 151 157 )
(137 157 163 )
(173 193 199 )
(251 271 277 )
(257 277 283 )
(311 331 337 )
(347 367 373 )
(353 373 379 )
(521 541 547 )
(587 607 613 )
(593 613 619 )
(857 877 883 )
(971 991 997 )
(1013 1033 1039 )
(1097 1117 1123 )
(1103 1123 1129 )
(1277 1297 1303 )
(1301 1321 1327 )
(1427 1447 1453 )
(1433 1453 1459 )
(1523 1543 1549 )
(1601 1621 1627 )
(1637 1657 1663 )
(1721 1741 1747 )
(1733 1753 1759 )
(1847 1867 1873 )
(1973 1993 1999 )
(2063 2083 2089 )
(2111 2131 2137 )
(2267 2287 2293 )
(2351 2371 2377 )
(2357 2377 2383 )
(2447 2467 2473 )
(2531 2551 2557 )
(2657 2677 2683 )
(2663 2683 2689 )
(2687 2707 2713 )
(2693 2713 2719 )
(2777 2797 2803 )
(3041 3061 3067 )
(3491 3511 3517 )
(3617 3637 3643 )
(3671 3691 3697 )
(4001 4021 4027 )
(4073 4093 4099 )
(4133 4153 4159 )
(4337 4357 4363 )
(4421 4441 4447 )
(4493 4513 4519 )
(4637 4657 4663 )
(4703 4723 4729 )
(4931 4951 4957 )
(4967 4987 4993 )
(4973 4993 4999 )
(5081 5101 5107 )
(5087 5107 5113 )
(5387 5407 5413 )
(5393 5413 5419 )
(5417 5437 5443 )
(5501 5521 5527 )
(5717 5737 5743 )
(5801 5821 5827 )
(6047 6067 6073 )
(6053 6073 6079 )
(6317 6337 6343 )
(6353 6373 6379 )
(6551 6571 6577 )
(6653 6673 6679 )
(6803 6823 6829 )
(6971 6991 6997 )
(7187 7207 7213 )
(7193 7213 7219 )
(7853 7873 7879 )
(7907 7927 7933 )
(8243 8263 8269 )
(8291 8311 8317 )
(8501 8521 8527 )
(8693 8713 8719 )
(8867 8887 8893 )
(9161 9181 9187 )
(9257 9277 9283 )
(9323 9343 9349 )
(9371 9391 9397 )
(9377 9397 9403 )
(9413 9433 9439 )
(9623 9643 9649 )
(9791 9811 9817 )
命题：项差依次为20，6的3生素数组有无穷多，其中有的组中间可能还有其他素数。

ysr · 发表于 2026-4-1 13:52

在10000内的这样的素数组有83 组：
(19 41 47 )
(31 53 59 )
(61 83 89 )
(79 101 107 )
(109 131 137 )
(151 173 179 )
(211 233 239 )
(229 251 257 )
(241 263 269 )
(331 353 359 )
(421 443 449 )
(439 461 467 )
(541 563 569 )
(571 593 599 )
(619 641 647 )
(631 653 659 )
(859 881 887 )
(919 941 947 )
(991 1013 1019 )
(1069 1091 1097 )
(1201 1223 1229 )
(1279 1301 1307 )
(1459 1481 1487 )
(1471 1493 1499 )
(1531 1553 1559 )
(1579 1601 1607 )
(1879 1901 1907 )
(1951 1973 1979 )
(2311 2333 2339 )
(2371 2393 2399 )
(2389 2411 2417 )
(2521 2543 2549 )
(2671 2693 2699 )
(3061 3083 3089 )
(3181 3203 3209 )
(3229 3251 3257 )
(3301 3323 3329 )
(3511 3533 3539 )
(3739 3761 3767 )
(3889 3911 3917 )
(4051 4073 4079 )
(4111 4133 4139 )
(4231 4253 4259 )
(4261 4283 4289 )
(4621 4643 4649 )
(4651 4673 4679 )
(4909 4931 4937 )
(5059 5081 5087 )
(5209 5231 5237 )
(5281 5303 5309 )
(5449 5471 5477 )
(5479 5501 5507 )
(5689 5711 5717 )
(5779 5801 5807 )
(5821 5843 5849 )
(5839 5861 5867 )
(6301 6323 6329 )
(6841 6863 6869 )
(6949 6971 6977 )
(6991 7013 7019 )
(7459 7481 7487 )
(7561 7583 7589 )
(7621 7643 7649 )
(7879 7901 7907 )
(8059 8081 8087 )
(8089 8111 8117 )
(8209 8231 8237 )
(8269 8291 8297 )
(8641 8663 8669 )
(8719 8741 8747 )
(8839 8861 8867 )
(8941 8963 8969 )
(9181 9203 9209 )
(9199 9221 9227 )
(9349 9371 9377 )
(9391 9413 9419 )
(9439 9461 9467 )
(9511 9533 9539 )
(9601 9623 9629 )
(9721 9743 9749 )
(9811 9833 9839 )
(9829 9851 9857 )
(9901 9923 9929 )
命题：项差依次为22，6的3生素数组有无穷多，其中有的组中间可能还有其他素数。

ysr · 发表于 2026-4-1 13:53

本帖最后由 ysr 于 2026-4-1 05:54 编辑

在10000内的这样的素数组有164 组：
(7 31 37 )
(13 37 43 )
(17 41 47 )
(23 47 53 )
(29 53 59 )
(37 61 67 )
(43 67 73 )
(59 83 89 )
(73 97 103 )
(79 103 109 )
(83 107 113 )
(107 131 137 )
(127 151 157 )
(149 173 179 )
(167 191 197 )
(199 223 229 )
(227 251 257 )
(233 257 263 )
(239 263 269 )
(283 307 313 )
(307 331 337 )
(349 373 379 )
(359 383 389 )
(409 433 439 )
(419 443 449 )
(433 457 463 )
(479 503 509 )
(547 571 577 )
(563 587 593 )
(569 593 599 )
(577 601 607 )
(617 641 647 )
(653 677 683 )
(709 733 739 )
(727 751 757 )
(797 821 827 )
(829 853 859 )
(853 877 883 )
(857 881 887 )
(947 971 977 )
(953 977 983 )
(967 991 997 )
(1009 1033 1039 )
(1039 1063 1069 )
(1063 1087 1093 )
(1093 1117 1123 )
(1163 1187 1193 )
(1193 1217 1223 )
(1259 1283 1289 )
(1277 1301 1307 )
(1297 1321 1327 )
(1399 1423 1429 )
(1409 1433 1439 )
(1423 1447 1453 )
(1429 1453 1459 )
(1459 1483 1489 )
(1583 1607 1613 )
(1597 1621 1627 )
(1669 1693 1699 )
(1723 1747 1753 )
(1753 1777 1783 )
(1759 1783 1789 )
(1847 1871 1877 )
(1877 1901 1907 )
(1949 1973 1979 )
(1973 1997 2003 )
(1987 2011 2017 )
(2039 2063 2069 )
(2113 2137 2143 )
(2213 2237 2243 )
(2243 2267 2273 )
(2309 2333 2339 )
(2347 2371 2377 )
(2393 2417 2423 )
(2417 2441 2447 )
(2633 2657 2663 )
(2647 2671 2677 )
(2659 2683 2689 )
(2663 2687 2693 )
(2683 2707 2713 )
(2689 2713 2719 )
(2767 2791 2797 )
(2879 2903 2909 )
(2939 2963 2969 )
(3037 3061 3067 )
(3229 3253 3259 )
(3299 3323 3329 )
(3433 3457 3463 )
(3517 3541 3547 )
(3583 3607 3613 )
(3593 3617 3623 )
(3607 3631 3637 )
(3613 3637 3643 )
(3709 3733 3739 )
(3823 3847 3853 )
(3989 4013 4019 )
(4027 4051 4057 )
(4049 4073 4079 )
(4129 4153 4159 )
(4229 4253 4259 )
(4259 4283 4289 )
(4483 4507 4513 )
(4493 4517 4523 )
(4567 4591 4597 )
(4649 4673 4679 )
(4759 4783 4789 )
(4943 4967 4973 )
(4969 4993 4999 )
(5077 5101 5107 )
(5273 5297 5303 )
(5279 5303 5309 )
(5407 5431 5437 )
(5413 5437 5443 )
(5419 5443 5449 )
(5477 5501 5507 )
(5623 5647 5653 )
(5659 5683 5689 )
(5783 5807 5813 )
(5827 5851 5857 )
(6043 6067 6073 )
(6173 6197 6203 )
(6247 6271 6277 )
(6287 6311 6317 )
(6299 6323 6329 )
(6329 6353 6359 )
(6337 6361 6367 )
(6343 6367 6373 )
(6397 6421 6427 )
(6547 6571 6577 )
(6679 6703 6709 )
(6803 6827 6833 )
(6833 6857 6863 )
(6947 6971 6977 )
(6967 6991 6997 )
(7079 7103 7109 )
(7213 7237 7243 )
(7457 7481 7487 )
(7499 7523 7529 )
(7517 7541 7547 )
(7559 7583 7589 )
(7793 7817 7823 )
(7853 7877 7883 )
(7877 7901 7907 )
(8087 8111 8117 )
(8093 8117 8123 )
(8263 8287 8293 )
(8287 8311 8317 )
(8513 8537 8543 )
(8599 8623 8629 )
(8669 8693 8699 )
(8689 8713 8719 )
(8707 8731 8737 )
(8807 8831 8837 )
(8837 8861 8867 )
(8863 8887 8893 )
(9103 9127 9133 )
(9127 9151 9157 )
(9157 9181 9187 )
(9319 9343 9349 )
(9437 9461 9467 )
(9467 9491 9497 )
(9619 9643 9649 )
(9719 9743 9749 )
(9787 9811 9817 )
命题：项差依次为24，6的3生素数组有无穷多，其中有的组中间可能还有其他素数。

ysr · 发表于 2026-4-1 13:56

在10000内的这样的素数组有65 组：
(5 31 37 )
(11 37 43 )
(41 67 73 )
(47 73 79 )
(71 97 103 )
(131 157 163 )
(167 193 199 )
(197 223 229 )
(251 277 283 )
(281 307 313 )
(347 373 379 )
(431 457 463 )
(587 613 619 )
(701 727 733 )
(797 823 829 )
(827 853 859 )
(1061 1087 1093 )
(1091 1117 1123 )
(1097 1123 1129 )
(1427 1453 1459 )
(1637 1663 1669 )
(1667 1693 1699 )
(1721 1747 1753 )
(1847 1873 1879 )
(2111 2137 2143 )
(2351 2377 2383 )
(2357 2383 2389 )
(2441 2467 2473 )
(2657 2683 2689 )
(2687 2713 2719 )
(3137 3163 3169 )
(3581 3607 3613 )
(3701 3727 3733 )
(3821 3847 3853 )
(4127 4153 4159 )
(4481 4507 4513 )
(4877 4903 4909 )
(4967 4993 4999 )
(5081 5107 5113 )
(5087 5113 5119 )
(5381 5407 5413 )
(5387 5413 5419 )
(5417 5443 5449 )
(5531 5557 5563 )
(5657 5683 5689 )
(5711 5737 5743 )
(5717 5743 5749 )
(6011 6037 6043 )
(6047 6073 6079 )
(6311 6337 6343 )
(6521 6547 6553 )
(7187 7213 7219 )
(7211 7237 7243 )
(7691 7717 7723 )
(7727 7753 7759 )
(7841 7867 7873 )
(7901 7927 7933 )
(8237 8263 8269 )
(8597 8623 8629 )
(8681 8707 8713 )
(8861 8887 8893 )
(9311 9337 9343 )
(9371 9397 9403 )
(9587 9613 9619 )
(9941 9967 9973 )
命题：项差依次为26，6的3生素数组有无穷多，其中有的组中间可能还有其他素数。

ysr · 发表于 2026-4-1 13:57

在10000内的这样的素数组有77 组：
(3 31 37 )
(13 41 47 )
(19 47 53 )
(73 101 107 )
(79 107 113 )
(103 131 137 )
(139 167 173 )
(163 191 197 )
(199 227 233 )
(223 251 257 )
(229 257 263 )
(283 311 317 )
(433 461 467 )
(613 641 647 )
(619 647 653 )
(829 857 863 )
(853 881 887 )
(919 947 953 )
(1063 1091 1097 )
(1069 1097 1103 )
(1153 1181 1187 )
(1249 1277 1283 )
(1399 1427 1433 )
(1453 1481 1487 )
(1459 1487 1493 )
(1579 1607 1613 )
(1873 1901 1907 )
(1879 1907 1913 )
(2053 2081 2087 )
(2179 2207 2213 )
(2239 2267 2273 )
(2383 2411 2417 )
(2389 2417 2423 )
(2659 2687 2693 )
(3433 3461 3467 )
(3499 3527 3533 )
(3643 3671 3677 )
(3733 3761 3767 )
(3769 3797 3803 )
(3889 3917 3923 )
(4099 4127 4133 )
(4363 4391 4397 )
(4423 4451 4457 )
(4759 4787 4793 )
(4903 4931 4937 )
(4909 4937 4943 )
(5119 5147 5153 )
(5443 5471 5477 )
(5449 5477 5483 )
(5623 5651 5657 )
(5683 5711 5717 )
(5779 5807 5813 )
(5869 5897 5903 )
(5953 5981 5987 )
(6229 6257 6263 )
(6829 6857 6863 )
(6883 6911 6917 )
(6949 6977 6983 )
(7159 7187 7193 )
(7219 7247 7253 )
(7489 7517 7523 )
(7549 7577 7583 )
(7789 7817 7823 )
(7873 7901 7907 )
(8053 8081 8087 )
(8059 8087 8093 )
(8089 8117 8123 )
(8209 8237 8243 )
(8263 8291 8297 )
(8713 8741 8747 )
(8719 8747 8753 )
(8803 8831 8837 )
(9343 9371 9377 )
(9403 9431 9437 )
(9433 9461 9467 )
(9439 9467 9473 )
(9463 9491 9497 )
命题：项差依次为28，6的3生素数组有无穷多，其中有的组中间可能还有其他素数。

代码如下：
Private Function fenjieyinzi(sa As String) As String
Dim x, a, b, k As String
a = Val(sa)

x = 3
If a <= 1 Or a > Int(a) Then
If a = 1 Then
fenjieyinzi = "它既不是质数，也不是合数"

Else
MsgBox "error"
End If

Else

Do While a / 2 = Int(a / 2) And a >= 4

If b = 0 Then
fenjieyinzi = fenjieyinzi & "2"
b = 1
Else
fenjieyinzi = fenjieyinzi & "*2"
End If
a = a / 2
k = a

Loop

Do While a > 1
Do While x <= Sqr(a)
Do While a / x = Int(a / x) And a >= x * x

If b = 0 Then
fenjieyinzi = fenjieyinzi & x
b = 1
Else
fenjieyinzi = fenjieyinzi & "*" & x
End If
a = a / x
Loop

x = x + 2
Loop

k = a
a = 1
Loop

If b = 1 Then
fenjieyinzi = fenjieyinzi & "*" & k
Else
fenjieyinzi = "这是一个质数"
End If





End If

End Function

Private Sub Command1_Click()
Dim a, b
a = Val(Text1)
p1 = 3
Do While p1 <= a
p1 = p1: p2 = p1 + 28: p3 = p2 + 6
p4 = p3 + 4: p5 = p4 + 210: p6 = p5 + 210: p7 = p6 + 210

p11 = fenjieyinzi(Val(p1)): p12 = fenjieyinzi(Val(p2)): p13 = fenjieyinzi(Val(p3))
p14 = fenjieyinzi(Val(p4)): p15 = fenjieyinzi(Val(p5)): p16 = fenjieyinzi(Val(p6)): p17 = fenjieyinzi(Val(p7))

If InStr(p11, "*") = 0 And InStr(p12, "*") = 0 And InStr(p13, "*") = 0 And InStr(p4, "*") = 0 And InStr(p5, "*") = 0 And InStr(p6, "*") = 0 And InStr(p7, "*") = 0 Then
s11 = s11 & "(" & p1 & " " & p2 & " " & p3 & " )  " & vbCrLf

s12 = s12 + 1
End If

p1 = p1 + 2
Loop
If s12 >= 1 Then
Text2 = "在" & Text1 & "内的这样的素数组有" & s12 & " 组： " & vbCrLf & s11
Else
Text2 = "wu  jie"
End If

Combo1 = Text2

End Sub

Private Sub Command2_Click()
Text1 = ""
Text2 = ""
Text3 = ""
Combo1 = ""
Form21.Cls
End Sub

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