基础理论中的两个重要定理的证明

ysr · 发表于 2026-4-1 09:20

在10000内的这样的素数组有114 组：
(5 29 53 )
(13 37 61 )
(19 43 67 )
(23 47 71 )
(59 83 107 )
(79 103 127 )
(83 107 131 )
(89 113 137 )
(103 127 151 )
(149 173 197 )
(233 257 281 )
(269 293 317 )
(283 307 331 )
(349 373 397 )
(373 397 421 )
(409 433 457 )
(419 443 467 )
(439 463 487 )
(443 467 491 )
(499 523 547 )
(523 547 571 )
(569 593 617 )
(593 617 641 )
(653 677 701 )
(709 733 757 )
(773 797 821 )
(829 853 877 )
(839 863 887 )
(859 883 907 )
(863 887 911 )
(929 953 977 )
(1039 1063 1087 )
(1069 1093 1117 )
(1259 1283 1307 )
(1279 1303 1327 )
(1399 1423 1447 )
(1423 1447 1471 )
(1559 1583 1607 )
(1699 1723 1747 )
(1753 1777 1801 )
(1823 1847 1871 )
(1949 1973 1997 )
(1979 2003 2027 )
(2039 2063 2087 )
(2063 2087 2111 )
(2089 2113 2137 )
(2113 2137 2161 )
(2309 2333 2357 )
(2333 2357 2381 )
(2393 2417 2441 )
(2399 2423 2447 )
(2609 2633 2657 )
(2659 2683 2707 )
(2663 2687 2711 )
(2683 2707 2731 )
(2729 2753 2777 )
(2753 2777 2801 )
(2879 2903 2927 )
(3299 3323 3347 )
(3323 3347 3371 )
(3533 3557 3581 )
(3559 3583 3607 )
(3583 3607 3631 )
(3919 3943 3967 )
(4003 4027 4051 )
(4129 4153 4177 )
(4153 4177 4201 )
(4349 4373 4397 )
(4373 4397 4421 )
(4909 4933 4957 )
(4919 4943 4967 )
(5393 5417 5441 )
(5479 5503 5527 )
(5483 5507 5531 )
(5669 5693 5717 )
(5693 5717 5741 )
(5879 5903 5927 )
(6043 6067 6091 )
(6173 6197 6221 )
(6263 6287 6311 )
(6373 6397 6421 )
(6529 6553 6577 )
(6779 6803 6827 )
(7079 7103 7127 )
(7103 7127 7151 )
(7283 7307 7331 )
(7369 7393 7417 )
(7433 7457 7481 )
(7499 7523 7547 )
(7559 7583 7607 )
(7793 7817 7841 )
(7829 7853 7877 )
(7853 7877 7901 )
(8069 8093 8117 )
(8123 8147 8171 )
(8263 8287 8311 )
(8269 8293 8317 )
(8329 8353 8377 )
(8419 8443 8467 )
(8599 8623 8647 )
(8689 8713 8737 )
(8713 8737 8761 )
(8783 8807 8831 )
(8839 8863 8887 )
(9043 9067 9091 )
(9103 9127 9151 )
(9109 9133 9157 )
(9133 9157 9181 )
(9413 9437 9461 )
(9473 9497 9521 )
(9719 9743 9767 )
(9743 9767 9791 )
(9859 9883 9907 )
(9883 9907 9931 )
公差为24的素数组，每一组中间还可能有其他素数

公差为3的倍数的偶数公差都有这样的3生素数组，每一组中间还可能有其他素数

ysr · 发表于 2026-4-1 09:24

在10000内的这样的素数组有223 组：
(7 37 67 )
(11 41 71 )
(13 43 73 )
(23 53 83 )
(29 59 89 )
(37 67 97 )
(41 71 101 )
(43 73 103 )
(53 83 113 )
(67 97 127 )
(71 101 131 )
(79 109 139 )
(97 127 157 )
(107 137 167 )
(137 167 197 )
(151 181 211 )
(163 193 223 )
(167 197 227 )
(181 211 241 )
(197 227 257 )
(211 241 271 )
(233 263 293 )
(251 281 311 )
(277 307 337 )
(307 337 367 )
(337 367 397 )
(349 379 409 )
(359 389 419 )
(379 409 439 )
(389 419 449 )
(401 431 461 )
(419 449 479 )
(431 461 491 )
(449 479 509 )
(461 491 521 )
(541 571 601 )
(547 577 607 )
(557 587 617 )
(571 601 631 )
(587 617 647 )
(601 631 661 )
(613 643 673 )
(617 647 677 )
(631 661 691 )
(709 739 769 )
(727 757 787 )
(797 827 857 )
(823 853 883 )
(827 857 887 )
(877 907 937 )
(881 911 941 )
(907 937 967 )
(911 941 971 )
(937 967 997 )
(953 983 1013 )
(991 1021 1051 )
(1009 1039 1069 )
(1031 1061 1091 )
(1033 1063 1093 )
(1063 1093 1123 )
(1093 1123 1153 )
(1163 1193 1223 )
(1171 1201 1231 )
(1229 1259 1289 )
(1259 1289 1319 )
(1399 1429 1459 )
(1423 1453 1483 )
(1429 1459 1489 )
(1451 1481 1511 )
(1493 1523 1553 )
(1523 1553 1583 )
(1549 1579 1609 )
(1553 1583 1613 )
(1567 1597 1627 )
(1597 1627 1657 )
(1607 1637 1667 )
(1637 1667 1697 )
(1663 1693 1723 )
(1693 1723 1753 )
(1723 1753 1783 )
(1801 1831 1861 )
(1847 1877 1907 )
(1871 1901 1931 )
(2039 2069 2099 )
(2053 2083 2113 )
(2069 2099 2129 )
(2081 2111 2141 )
(2083 2113 2143 )
(2207 2237 2267 )
(2213 2243 2273 )
(2221 2251 2281 )
(2237 2267 2297 )
(2251 2281 2311 )
(2281 2311 2341 )
(2311 2341 2371 )
(2351 2381 2411 )
(2381 2411 2441 )
(2417 2447 2477 )
(2549 2579 2609 )
(2617 2647 2677 )
(2633 2663 2693 )
(2647 2677 2707 )
(2659 2689 2719 )
(2689 2719 2749 )
(2857 2887 2917 )
(2879 2909 2939 )
(2897 2927 2957 )
(2909 2939 2969 )
(2939 2969 2999 )
(3019 3049 3079 )
(3049 3079 3109 )
(3191 3221 3251 )
(3271 3301 3331 )
(3299 3329 3359 )
(3301 3331 3361 )
(3313 3343 3373 )
(3329 3359 3389 )
(3331 3361 3391 )
(3469 3499 3529 )
(3499 3529 3559 )
(3511 3541 3571 )
(3583 3613 3643 )
(3613 3643 3673 )
(3709 3739 3769 )
(3793 3823 3853 )
(3803 3833 3863 )
(3821 3851 3881 )
(3847 3877 3907 )
(3851 3881 3911 )
(3989 4019 4049 )
(4019 4049 4079 )
(4099 4129 4159 )
(4201 4231 4261 )
(4211 4241 4271 )
(4229 4259 4289 )
(4297 4327 4357 )
(4391 4421 4451 )
(4421 4451 4481 )
(4463 4493 4523 )
(4561 4591 4621 )
(4591 4621 4651 )
(4643 4673 4703 )
(4673 4703 4733 )
(4691 4721 4751 )
(4729 4759 4789 )
(4801 4831 4861 )
(4943 4973 5003 )
(5021 5051 5081 )
(5167 5197 5227 )
(5273 5303 5333 )
(5419 5449 5479 )
(5441 5471 5501 )
(5471 5501 5531 )
(5623 5653 5683 )
(5783 5813 5843 )
(5791 5821 5851 )
(5821 5851 5881 )
(5867 5897 5927 )
(6007 6037 6067 )
(6091 6121 6151 )
(6113 6143 6173 )
(6143 6173 6203 )
(6217 6247 6277 )
(6257 6287 6317 )
(6269 6299 6329 )
(6299 6329 6359 )
(6329 6359 6389 )
(6337 6367 6397 )
(6367 6397 6427 )
(6421 6451 6481 )
(6491 6521 6551 )
(6521 6551 6581 )
(6547 6577 6607 )
(6577 6607 6637 )
(6659 6689 6719 )
(6673 6703 6733 )
(6703 6733 6763 )
(6733 6763 6793 )
(6763 6793 6823 )
(6803 6833 6863 )
(6917 6947 6977 )
(6967 6997 7027 )
(6983 7013 7043 )
(6997 7027 7057 )
(7177 7207 7237 )
(7457 7487 7517 )
(7477 7507 7537 )
(7487 7517 7547 )
(7499 7529 7559 )
(7517 7547 7577 )
(7529 7559 7589 )
(7547 7577 7607 )
(7561 7591 7621 )
(7639 7669 7699 )
(7643 7673 7703 )
(7793 7823 7853 )
(7823 7853 7883 )
(7877 7907 7937 )
(7933 7963 7993 )
(8009 8039 8069 )
(8087 8117 8147 )
(8161 8191 8221 )
(8233 8263 8293 )
(8513 8543 8573 )
(8647 8677 8707 )
(8677 8707 8737 )
(8807 8837 8867 )
(8863 8893 8923 )
(8941 8971 9001 )
(8969 8999 9029 )
(8999 9029 9059 )
(9127 9157 9187 )
(9281 9311 9341 )
(9311 9341 9371 )
(9403 9433 9463 )
(9431 9461 9491 )
(9437 9467 9497 )
(9461 9491 9521 )
(9491 9521 9551 )
(9601 9631 9661 )
(9619 9649 9679 )
(9689 9719 9749 )
(9871 9901 9931 )
公差为30的素数组，每一组中间还可能有其他素数

公差为3的偶数倍的时候都有这样的3生素数组，每一组中间还可能有其他素数

ysr · 发表于 2026-4-1 09:26

在10000内的这样的素数组有110 组：
(7 43 79 )
(11 47 83 )
(17 53 89 )
(31 67 103 )
(37 73 109 )
(67 103 139 )
(101 137 173 )
(127 163 199 )
(157 193 229 )
(191 227 263 )
(197 233 269 )
(241 277 313 )
(277 313 349 )
(281 317 353 )
(311 347 383 )
(317 353 389 )
(337 373 409 )
(347 383 419 )
(431 467 503 )
(521 557 593 )
(541 577 613 )
(571 607 643 )
(647 683 719 )
(751 787 823 )
(787 823 859 )
(911 947 983 )
(941 977 1013 )
(947 983 1019 )
(977 1013 1049 )
(997 1033 1069 )
(1051 1087 1123 )
(1151 1187 1223 )
(1187 1223 1259 )
(1451 1487 1523 )
(1487 1523 1559 )
(1621 1657 1693 )
(1627 1663 1699 )
(1877 1913 1949 )
(2017 2053 2089 )
(2027 2063 2099 )
(2237 2273 2309 )
(2311 2347 2383 )
(2467 2503 2539 )
(2521 2557 2593 )
(2621 2657 2693 )
(2647 2683 2719 )
(2657 2693 2729 )
(2677 2713 2749 )
(2731 2767 2803 )
(2927 2963 2999 )
(3181 3217 3253 )
(3271 3307 3343 )
(3511 3547 3583 )
(3571 3607 3643 )
(3637 3673 3709 )
(3697 3733 3769 )
(3761 3797 3833 )
(3931 3967 4003 )
(4021 4057 4093 )
(4057 4093 4129 )
(4217 4253 4289 )
(4337 4373 4409 )
(4421 4457 4493 )
(4447 4483 4519 )
(4567 4603 4639 )
(4931 4967 5003 )
(4937 4973 5009 )
(4951 4987 5023 )
(4967 5003 5039 )
(4987 5023 5059 )
(5237 5273 5309 )
(5261 5297 5333 )
(5407 5443 5479 )
(5807 5843 5879 )
(5867 5903 5939 )
(6007 6043 6079 )
(6287 6323 6359 )
(6301 6337 6373 )
(6317 6353 6389 )
(6637 6673 6709 )
(6791 6827 6863 )
(6827 6863 6899 )
(6911 6947 6983 )
(6947 6983 7019 )
(7211 7247 7283 )
(7297 7333 7369 )
(7451 7487 7523 )
(7487 7523 7559 )
(7681 7717 7753 )
(7687 7723 7759 )
(7717 7753 7789 )
(7757 7793 7829 )
(8017 8053 8089 )
(8317 8353 8389 )
(8501 8537 8573 )
(8527 8563 8599 )
(8537 8573 8609 )
(8627 8663 8699 )
(8641 8677 8713 )
(8747 8783 8819 )
(8971 9007 9043 )
(9137 9173 9209 )
(9221 9257 9293 )
(9341 9377 9413 )
(9461 9497 9533 )
(9551 9587 9623 )
(9661 9697 9733 )
(9697 9733 9769 )
(9767 9803 9839 )
(9851 9887 9923 )
公差为36的素数组，每一组中间还可能有其他素数

ysr · 发表于 2026-4-1 09:28

在10000内的这样的素数组有118 组：
(5 11 17 )
(7 13 19 )
(11 17 23 )
(17 23 29 )
(31 37 43 )
(41 47 53 )
(47 53 59 )
(61 67 73 )
(67 73 79 )
(97 103 109 )
(101 107 113 )
(151 157 163 )
(167 173 179 )
(227 233 239 )
(251 257 263 )
(257 263 269 )
(271 277 283 )
(347 353 359 )
(367 373 379 )
(557 563 569 )
(587 593 599 )
(601 607 613 )
(607 613 619 )
(641 647 653 )
(647 653 659 )
(727 733 739 )
(941 947 953 )
(971 977 983 )
(1091 1097 1103 )
(1097 1103 1109 )
(1117 1123 1129 )
(1181 1187 1193 )
(1217 1223 1229 )
(1277 1283 1289 )
(1291 1297 1303 )
(1361 1367 1373 )
(1427 1433 1439 )
(1447 1453 1459 )
(1481 1487 1493 )
(1487 1493 1499 )
(1601 1607 1613 )
(1607 1613 1619 )
(1657 1663 1669 )
(1741 1747 1753 )
(1747 1753 1759 )
(1777 1783 1789 )
(1861 1867 1873 )
(1867 1873 1879 )
(1901 1907 1913 )
(1987 1993 1999 )
(2131 2137 2143 )
(2281 2287 2293 )
(2371 2377 2383 )
(2377 2383 2389 )
(2411 2417 2423 )
(2671 2677 2683 )
(2677 2683 2689 )
(2687 2693 2699 )
(2707 2713 2719 )
(2791 2797 2803 )
(2897 2903 2909 )
(2957 2963 2969 )
(3301 3307 3313 )
(3307 3313 3319 )
(3457 3463 3469 )
(3527 3533 3539 )
(3631 3637 3643 )
(3727 3733 3739 )
(3911 3917 3923 )
(3917 3923 3929 )
(4001 4007 4013 )
(4007 4013 4019 )
(4127 4133 4139 )
(4451 4457 4463 )
(4507 4513 4519 )
(4591 4597 4603 )
(4637 4643 4649 )
(4651 4657 4663 )
(4787 4793 4799 )
(4931 4937 4943 )
(4987 4993 4999 )
(5101 5107 5113 )
(5107 5113 5119 )
(5297 5303 5309 )
(5381 5387 5393 )
(5387 5393 5399 )
(5407 5413 5419 )
(5431 5437 5443 )
(5437 5443 5449 )
(5471 5477 5483 )
(5557 5563 5569 )
(5641 5647 5653 )
(5647 5653 5659 )
(5737 5743 5749 )
(5801 5807 5813 )
(6067 6073 6079 )
(6257 6263 6269 )
(6311 6317 6323 )
(6317 6323 6329 )
(6361 6367 6373 )
(6367 6373 6379 )
(6857 6863 6869 )
(6971 6977 6983 )
(7207 7213 7219 )
(7517 7523 7529 )
(7577 7583 7589 )
(7817 7823 7829 )
(7867 7873 7879 )
(8081 8087 8093 )
(8111 8117 8123 )
(8231 8237 8243 )
(8707 8713 8719 )
(8741 8747 8753 )
(9001 9007 9013 )
(9337 9343 9349 )
(9391 9397 9403 )
(9461 9467 9473 )
(9467 9473 9479 )
公差为6的素数组，有的组中间还可能有其他素数

ysr · 发表于 2026-4-1 10:51

在10000内的这样的素数组有166 组：
(5 47 89 )
(17 59 101 )
(19 61 103 )
(29 71 113 )
(47 89 131 )
(67 109 151 )
(89 131 173 )
(97 139 181 )
(107 149 191 )
(109 151 193 )
(139 181 223 )
(149 191 233 )
(157 199 241 )
(197 239 281 )
(199 241 283 )
(227 269 311 )
(229 271 313 )
(269 311 353 )
(317 359 401 )
(337 379 421 )
(347 389 431 )
(359 401 443 )
(379 421 463 )
(419 461 503 )
(457 499 541 )
(479 521 563 )
(557 599 641 )
(577 619 661 )
(599 641 683 )
(617 659 701 )
(659 701 743 )
(677 719 761 )
(727 769 811 )
(769 811 853 )
(797 839 881 )
(887 929 971 )
(929 971 1013 )
(967 1009 1051 )
(977 1019 1061 )
(1009 1051 1093 )
(1019 1061 1103 )
(1087 1129 1171 )
(1109 1151 1193 )
(1129 1171 1213 )
(1217 1259 1301 )
(1237 1279 1321 )
(1277 1319 1361 )
(1367 1409 1451 )
(1409 1451 1493 )
(1439 1481 1523 )
(1447 1489 1531 )
(1579 1621 1663 )
(1657 1699 1741 )
(1699 1741 1783 )
(1747 1789 1831 )
(1789 1831 1873 )
(1847 1889 1931 )
(1889 1931 1973 )
(1997 2039 2081 )
(2027 2069 2111 )
(2069 2111 2153 )
(2137 2179 2221 )
(2267 2309 2351 )
(2297 2339 2381 )
(2309 2351 2393 )
(2339 2381 2423 )
(2357 2399 2441 )
(2549 2591 2633 )
(2579 2621 2663 )
(2647 2689 2731 )
(2657 2699 2741 )
(2707 2749 2791 )
(2749 2791 2833 )
(2777 2819 2861 )
(2819 2861 2903 )
(2927 2969 3011 )
(2957 2999 3041 )
(2999 3041 3083 )
(3037 3079 3121 )
(3079 3121 3163 )
(3167 3209 3251 )
(3187 3229 3271 )
(3217 3259 3301 )
(3229 3271 3313 )
(3259 3301 3343 )
(3329 3371 3413 )
(3407 3449 3491 )
(3449 3491 3533 )
(3457 3499 3541 )
(3499 3541 3583 )
(3529 3571 3613 )
(3539 3581 3623 )
(3617 3659 3701 )
(3677 3719 3761 )
(3719 3761 3803 )
(3779 3821 3863 )
(3847 3889 3931 )
(4007 4049 4091 )
(4049 4091 4133 )
(4159 4201 4243 )
(4177 4219 4261 )
(4409 4451 4493 )
(4507 4549 4591 )
(4519 4561 4603 )
(4637 4679 4721 )
(4649 4691 4733 )
(4889 4931 4973 )
(4909 4951 4993 )
(4967 5009 5051 )
(5147 5189 5231 )
(5189 5231 5273 )
(5309 5351 5393 )
(5399 5441 5483 )
(5437 5479 5521 )
(5479 5521 5563 )
(5659 5701 5743 )
(5737 5779 5821 )
(5839 5881 5923 )
(5897 5939 5981 )
(6037 6079 6121 )
(6047 6089 6131 )
(6079 6121 6163 )
(6089 6131 6173 )
(6269 6311 6353 )
(6337 6379 6421 )
(6577 6619 6661 )
(6619 6661 6703 )
(6719 6761 6803 )
(6827 6869 6911 )
(6907 6949 6991 )
(6917 6959 7001 )
(6959 7001 7043 )
(7109 7151 7193 )
(7309 7351 7393 )
(7457 7499 7541 )
(7499 7541 7583 )
(7507 7549 7591 )
(7607 7649 7691 )
(7639 7681 7723 )
(8017 8059 8101 )
(8039 8081 8123 )
(8179 8221 8263 )
(8269 8311 8353 )
(8377 8419 8461 )
(8539 8581 8623 )
(8647 8689 8731 )
(8677 8719 8761 )
(8699 8741 8783 )
(8719 8761 8803 )
(8737 8779 8821 )
(8779 8821 8863 )
(8887 8929 8971 )
(8929 8971 9013 )
(9007 9049 9091 )
(9049 9091 9133 )
(9067 9109 9151 )
(9157 9199 9241 )
(9199 9241 9283 )
(9239 9281 9323 )
(9349 9391 9433 )
(9377 9419 9461 )
(9437 9479 9521 )
(9697 9739 9781 )
(9749 9791 9833 )
(9787 9829 9871 )
(9817 9859 9901 )
公差为42的素数组，每一组中间还可能有其他素数

ysr · 发表于 2026-4-1 11:03

命题：公差为3的偶数倍的3生素数组有无穷多组，其中有的素数组中间还可能有其他素数。

ysr · 发表于 2026-4-1 11:10

在10000内的这样的素数组有24 组：
(5 11 17 23 )
(11 17 23 29 )
(41 47 53 59 )
(61 67 73 79 )
(251 257 263 269 )
(601 607 613 619 )
(641 647 653 659 )
(1091 1097 1103 1109 )
(1481 1487 1493 1499 )
(1601 1607 1613 1619 )
(1741 1747 1753 1759 )
(1861 1867 1873 1879 )
(2371 2377 2383 2389 )
(2671 2677 2683 2689 )
(3301 3307 3313 3319 )
(3911 3917 3923 3929 )
(4001 4007 4013 4019 )
(5101 5107 5113 5119 )
(5381 5387 5393 5399 )
(5431 5437 5443 5449 )
(5641 5647 5653 5659 )
(6311 6317 6323 6329 )
(6361 6367 6373 6379 )
(9461 9467 9473 9479 )
公差为6的素数组，有的组中间还可能有其他素数

ysr · 发表于 2026-4-1 11:12

命题：公差为6的4生素数组有无穷多组，其中有的组中间还可能有其他素数。

ysr · 发表于 2026-4-1 11:15

在10000内的这样的素数组有27 组：
(5 17 29 41 )
(7 19 31 43 )
(17 29 41 53 )
(47 59 71 83 )
(127 139 151 163 )
(227 239 251 263 )
(257 269 281 293 )
(397 409 421 433 )
(467 479 491 503 )
(607 619 631 643 )
(997 1009 1021 1033 )
(1447 1459 1471 1483 )
(1487 1499 1511 1523 )
(1697 1709 1721 1733 )
(1877 1889 1901 1913 )
(2647 2659 2671 2683 )
(3307 3319 3331 3343 )
(3547 3559 3571 3583 )
(3907 3919 3931 3943 )
(4217 4229 4241 4253 )
(4987 4999 5011 5023 )
(5407 5419 5431 5443 )
(6287 6299 6311 6323 )
(6947 6959 6971 6983 )
(7297 7309 7321 7333 )
(7537 7549 7561 7573 )
(7817 7829 7841 7853 )
公差为12的素数组，有的组中间还可能有其他素数

ysr · 发表于 2026-4-1 11:15

命题：公差为12的4生素数组有无穷多组，其中有的组中间还可能有其他素数。

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