2024-03-12 09:36:06
7 = 30 - 23
11 = 30 - 19 = 210 - 199
13 = 30 - 17 = 210 - 197 = 2310 - 2297
17 = 30 - 13 = 210 - 193 = 2310 - 2293 = 30030 - 30013
19 = 30 - 11 = 210 - 191 = 30030 - 30011
23 = 30 - 7 = 2310 - 2287
29 = 210 - 181 = 2310 - 2281 = 510510 - 510481
31 = 210 - 179
37 = 210 - 173 = 2310 - 2273
41 = 2310 - 2269 = 30030 - 29989
43 = 210 - 167 = 2310 - 2267
47 = 210 - 163 = 30030 - 29983 = 510510 - 510463
53 = 210 - 157 = 510510 - 510457
59 = 210 - 151 = 2310 - 2251 = 510510 - 510451
61 = 210 - 149 = 510510 - 510449
67 = 2310 - 2243
71 = 210 - 139 = 2310 - 2239 = 30030 - 29959
73 = 210 - 137 = 2310 - 2237
79 = 210 - 131
83 = 210 - 127 = 30030 - 29947
89 = 2310 - 2221
97 = 210 - 113 = 2310 - 2213
101 = 210 - 109
103 = 210 - 107 = 2310 - 2207 = 30030 - 29927
107 = 210 - 103 = 2310 - 2203 = 510510 - 510403
109 = 210 - 101 = 30030 - 29921 = 510510 - 510401
113 = 210 - 97 = 30030 - 29917
127 = 210 - 83 = 510510 - 510383
131 = 210 - 79 = 2310 - 2179 = 510510 - 510379
137 = 210 - 73
139 = 210 - 71
149 = 210 - 61 = 2310 - 2161 = 30030 - 29881 = 510510 - 510361
151 = 210 - 59 = 30030 - 29879
157 = 210 - 53 = 2310 - 2153 = 30030 - 29873
163 = 210 - 47 = 30030 - 29867
167 = 210 - 43 = 2310 - 2143 = 30030 - 29863
173 = 210 - 37 = 2310 - 2137
179 = 210 - 31 = 2310 - 2131 = 30030 - 29851 = 510510 - 510331
181 = 210 - 29 = 2310 - 2129
191 = 210 - 19 = 510510 - 510319
193 = 210 - 17 = 30030 - 29837
197 = 210 - 13 = 2310 - 2113 = 30030 - 29833
199 = 210 - 11 = 2310 - 2111 = 510510 - 510311
211 = 2310 - 2099 = 30030 - 29819 = 510510 - 510299
223 = 2310 - 2087 = 510510 - 510287
227 = 2310 - 2083 = 30030 - 29803
229 = 2310 - 2081
233 = 7858321551080267055879090 - 7858321551080267055878857
239 = 510510 - 510271
241 = 2310 - 2069 = 30030 - 29789
251 = 200560490130 - 200560489879
257 = 2310 - 2053 = 510510 - 510253
263 = 510510 - 510247
269 = 30030 - 29761 = 510510 - 510241
271 = 2310 - 2039 = 30030 - 29759
277 = 30030 - 29753 = 510510 - 510233
281 = 2310 - 2029
283 = 2310 - 2027 = 510510 - 510227
293 = 2310 - 2017 = 510510 - 510217
307 = 2310 - 2003 = 30030 - 29723 = 510510 - 510203
311 = 2310 - 1999 = 510510 - 510199
313 = 2310 - 1997 = 30030 - 29717
317 = 2310 - 1993
331 = 2310 - 1979 = 510510 - 510179
337 = 2310 - 1973
347 = 30030 - 29683
349 = 9699690 - 9699341
353 = 510510 - 510157
359 = 2310 - 1951 = 30030 - 29671
367 = 30030 - 29663
373 = 510510 - 510137
379 = 2310 - 1931
383 = 510510 - 510127
389 = 30030 - 29641 = 510510 - 510121
397 = 2310 - 1913 = 30030 - 29633
401 = 30030 - 29629
409 = 2310 - 1901 = 510510 - 510101
419 = 30030 - 29611
421 = 2310 - 1889 = 510510 - 510089
431 = 2310 - 1879 = 30030 - 29599 = 510510 - 510079
433 = 2310 - 1877 = 510510 - 510077
439 = 2310 - 1871
443 = 2310 - 1867 = 30030 - 29587 = 510510 - 510067
449 = 2310 - 1861 = 30030 - 29581 = 510510 - 510061
457 = 30030 - 29573
461 = 30030 - 29569 = 510510 - 510049
463 = 2310 - 1847 = 30030 - 29567 = 510510 - 510047
467 = 6469693230 - 6469692763
479 = 2310 - 1831 = 510510 - 510031
487 = 2310 - 1823
491 = 9699690 - 9699199
499 = 2310 - 1811 = 30030 - 29531

请举例说明。

接2楼
503 = 30030 - 29527
509 = 2310 - 1801
521 = 2310 - 1789
523 = 2310 - 1787
541 = 9699690(19#) - 9699149
547 = 30030 - 29483
557 = 2310 - 1753 = 30030 - 29473
563 = 2310 - 1747
569 = 2310 - 1741
571 = 510510(17#) - 509939
577 = 2310 - 1733 = 30030 - 29453
587 = 2310 - 1723 = 30030 - 29443
593 = 30030 - 29437
599 = 510510(17#) - 509911
601 = 2310 - 1709 = 30030 - 29429
607 = 30030 - 29423
613 = 2310 - 1697
617 = 2310 - 1693
619 = 30030 - 29411
631 = 30030 - 29399
641 = 2310 - 1669 = 30030 - 29389
643 = 2310 - 1667 = 30030 - 29387
647 = 2310 - 1663 = 30030 - 29383
653 = 2310 - 1657
659 = 6469693230(29#) - 6469692571
661 = 223092870(23#) - 223092209
673 = 2310 - 1637
677 = 510510(17#) - 509833
683 = 2310 - 1627 = 30030 - 29347
691 = 2310 - 1619 = 30030 - 29339
701 = 2310 - 1609
709 = 2310 - 1601
719 = 30030 - 29311
727 = 2310 - 1583 = 30030 - 29303
733 = 30030 - 29297
739 = 2310 - 1571
743 = 2310 - 1567 = 30030 - 29287
751 = 2310 - 1559
757 = 2310 - 1553
761 = 2310 - 1549 = 30030 - 29269
769 = 510510(17#) - 509741
773 = 510510(17#) - 509737
787 = 2310 - 1523 = 30030 - 29243
797 = 223092870(23#) - 223092073
809 = 30030 - 29221
811 = 2310 - 1499
821 = 2310 - 1489 = 30030 - 29209
823 = 2310 - 1487 = 30030 - 29207
827 = 2310 - 1483
829 = 2310 - 1481 = 30030 - 29201
839 = 2310 - 1471 = 30030 - 29191
853 = 223092870(23#) - 223092017
857 = 2310 - 1453 = 30030 - 29173
859 = 2310 - 1451
863 = 2310 - 1447 = 30030 - 29167
877 = 2310 - 1433 = 30030 - 29153
881 = 2310 - 1429
883 = 2310 - 1427 = 30030 - 29147
887 = 2310 - 1423
907 = 30030 - 29123
911 = 2310 - 1399
919 = 510510(17#) - 509591
929 = 2310 - 1381 = 30030 - 29101
937 = 2310 - 1373
941 = 510510(17#) - 509569
947 = 510510(17#) - 509563
953 = 30030 - 29077
967 = 30030 - 29063
971 = 30030 - 29059
977 = 9699690(19#) - 9698713
983 = 2310 - 1327
991 = 2310 - 1319
997 = 30030 - 29033
[]
用时 0.01563 秒

老话说的好，猜想的基本属性——找不到反例。
对于素数p，怎样找反例呢？
必须要把小于p的所有素数阶乘P#-p都验算一遍，如果它们都不是素数，才是反例。
找反例，是一项非常艰巨的工作。50000000以内无反例哦！

若变成p = P# + q又当如何？很难保证有解。
2024-03-14 22:29:14
5 = 2 + 3
7 = 2 + 5
11 = 6 + 5
13 = 2 + 11 = 6 + 7
17 = 6 + 11
19 = 2 + 17 = 6 + 13
23 = 6 + 17
29 = 6 + 23
31 = 2 + 29
37 = 6 + 31 = 30 + 7
41 = 30 + 11
43 = 2 + 41 = 6 + 37 = 30 + 13
47 = 6 + 41 = 30 + 17
53 = 6 + 47 = 30 + 23
59 = 6 + 53 = 30 + 29
61 = 2 + 59 = 30 + 31
67 = 6 + 61 = 30 + 37
71 = 30 + 41
73 = 2 + 71 = 6 + 67 = 30 + 43
79 = 6 + 73
83 = 30 + 53
89 = 6 + 83 = 30 + 59
97 = 30 + 67
101 = 30 + 71
103 = 2 + 101 = 6 + 97 = 30 + 73
107 = 6 + 101
109 = 2 + 107 = 6 + 103 = 30 + 79
113 = 6 + 107 = 30 + 83
127 = 30 + 97
131 = 30 + 101
137 = 6 + 131 = 30 + 107
139 = 2 + 137 = 30 + 109
149
151 = 2 + 149
157 = 6 + 151 = 30 + 127
163 = 6 + 157
167 = 30 + 137
173 = 6 + 167
179 = 6 + 173 = 30 + 149
181 = 2 + 179 = 30 + 151
191
193 = 2 + 191 = 30 + 163
197 = 6 + 191 = 30 + 167
199 = 2 + 197 = 6 + 193
211 = 30 + 181
223 = 30 + 193 = 210 + 13
227 = 30 + 197 = 210 + 17
229 = 2 + 227 = 6 + 223 = 30 + 199 = 210 + 19
233 = 6 + 227 = 210 + 23
239 = 6 + 233 = 210 + 29
241 = 2 + 239 = 30 + 211 = 210 + 31
251 = 210 + 41
257 = 6 + 251 = 30 + 227 = 210 + 47
263 = 6 + 257 = 30 + 233 = 210 + 53
269 = 6 + 263 = 30 + 239 = 210 + 59
271 = 2 + 269 = 30 + 241 = 210 + 61
277 = 6 + 271 = 210 + 67
281 = 30 + 251 = 210 + 71
283 = 2 + 281 = 6 + 277 = 210 + 73
293 = 30 + 263 = 210 + 83
307 = 30 + 277 = 210 + 97
311 = 30 + 281 = 210 + 101
313 = 2 + 311 = 6 + 307 = 30 + 283 = 210 + 103
317 = 6 + 311 = 210 + 107
331
337 = 6 + 331 = 30 + 307 = 210 + 127
347 = 30 + 317 = 210 + 137
349 = 2 + 347 = 210 + 139
353 = 6 + 347
359 = 6 + 353 = 210 + 149
367 = 30 + 337 = 210 + 157
373 = 6 + 367 = 210 + 163
379 = 6 + 373 = 30 + 349
383 = 30 + 353 = 210 + 173
389 = 6 + 383 = 30 + 359 = 210 + 179
397 = 30 + 367
401 = 210 + 191
409 = 30 + 379 = 210 + 199
419 = 30 + 389
421 = 2 + 419 = 210 + 211
431 = 30 + 401
433 = 2 + 431 = 210 + 223
439 = 6 + 433 = 30 + 409 = 210 + 229
443 = 210 + 233
449 = 6 + 443 = 30 + 419 = 210 + 239
457
461 = 30 + 431 = 210 + 251
463 = 2 + 461 = 6 + 457 = 30 + 433
467 = 6 + 461 = 210 + 257
479 = 30 + 449 = 210 + 269
487 = 30 + 457 = 210 + 277
491 = 30 + 461 = 210 + 281
499
用时 0.00100 秒

在p = P# - q中，显然q没有小于或等于P的素因子，必然又q>P；由对称性，也必然有p>P。
用通俗的话讲就是，任意大于5的素数都可以表示成，一个素数阶乘与一个素数的差。
题外话，大部分的素数都可以表示成，一个素数阶乘与一个素数的和。

猜想的另一个基本属性——还未被证明。
猜想一旦被证明，就不叫作猜想了，比如陈氏定理等。

300以内素数的全解，限于篇幅，具体素数显示省略。
2024-03-18 09:35:11
7 = 5# - {...}
11 = 5# - {...} = 7# - {...}
13 = 5# - {...} = 7# - {...} = 11# - {...}
17 = 5# - {...} = 7# - {...} = 11# - {...} = 13# - {...}
19 = 5# - {...} = 7# - {...} = 13# - {...}
23 = 5# - {...} = 11# - {...} = 19# - {...}
29 = 7# - {...} = 11# - {...} = 17# - {...}
31 = 7# - {...}
37 = 7# - {...} = 11# - {...} = 19# - {...}
41 = 11# - {...} = 13# - {...} = 19# - {...} = 29# - {...}
43 = 7# - {...} = 11# - {...} = 19# - {...} = 23# - {...}
47 = 7# - {...} = 13# - {...} = 17# - {...} = 19# - {...} = 41# - {...}
53 = 7# - {...} = 17# - {...} = 19# - {...} = 41# - {...}
59 = 7# - {...} = 11# - {...} = 17# - {...} = 19# - {...} = 37# - {...}
61 = 7# - {...} = 17# - {...} = 23# - {...}
67 = 11# - {...} = 19# - {...} = 29# - {...} = 47# - {...}
71 = 7# - {...} = 11# - {...} = 13# - {...} = 41# - {...}
73 = 7# - {...} = 11# - {...} = 29# - {...} = 31# - {...} = 53# - {...}
79 = 7# - {...} = 19# - {...} = 23# - {...} = 31# - {...}
83 = 7# - {...} = 13# - {...} = 31# - {...} = 79# - {...}
89 = 11# - {...} = 31# - {...} = 41# - {...} = 43# - {...} = 53# - {...} = 61# - {...} = 83# - {...}
97 = 7# - {...} = 11# - {...} = 19# - {...} = 23# - {...} = 31# - {...} = 47# - {...} = 73# - {...} = 89# - {...}
101 = 7# - {...} = 23# - {...} = 29# - {...} = 67# - {...} = 79# - {...} = 89# - {...}
103 = 7# - {...} = 11# - {...} = 13# - {...} = 41# - {...} = 89# - {...}
107 = 7# - {...} = 11# - {...} = 17# - {...} = 31# - {...} = 37# - {...} = 59# - {...} = 67# - {...}
109 = 7# - {...} = 13# - {...} = 17# - {...} = 59# - {...}
113 = 7# - {...} = 13# - {...} = 23# - {...} = 67# - {...} = 103# - {...}
127 = 7# - {...} = 17# - {...} = 19# - {...} = 23# - {...} = 31# - {...} = 53# - {...} = 67# - {...} = 71# - {...} = 79# - {...}
131 = 7# - {...} = 11# - {...} = 17# - {...} = 41# - {...} = 101# - {...}
137 = 7# - {...} = 23# - {...} = 41# - {...} = 53# - {...} = 79# - {...} = 103# - {...}
139 = 7# - {...} = 19# - {...} = 37# - {...} = 53# - {...} = 101# - {...}
149 = 7# - {...} = 11# - {...} = 13# - {...} = 17# - {...} = 29# - {...} = 31# - {...} = 43# - {...} = 89# - {...} = 101# - {...}
151 = 7# - {...} = 13# - {...} = 29# - {...} = 37# - {...} = 47# - {...} = 107# - {...} = 149# - {...}
157 = 7# - {...} = 11# - {...} = 13# - {...} = 19# - {...}
163 = 7# - {...} = 13# - {...} = 37# - {...} = 59# - {...} = 67# - {...}
167 = 7# - {...} = 11# - {...} = 13# - {...} = 43# - {...} = 47# - {...} = 59# - {...} = 79# - {...} = 101# - {...}
173 = 7# - {...} = 11# - {...} = 29# - {...} = 31# - {...} = 157# - {...}
179 = 7# - {...} = 11# - {...} = 13# - {...} = 17# - {...} = 19# - {...} = 29# - {...} = 71# - {...} = 131# - {...}
181 = 7# - {...} = 11# - {...} = 19# - {...} = 23# - {...} = 41# - {...} = 73# - {...}
191 = 7# - {...} = 17# - {...} = 53# - {...} = 59# - {...} = 73# - {...} = 79# - {...} = 173# - {...}
193 = 7# - {...} = 13# - {...} = 29# - {...} = 41# - {...} = 53# - {...}
197 = 7# - {...} = 11# - {...} = 13# - {...} = 23# - {...} = 31# - {...} = 41# - {...} = 83# - {...} = 107# - {...} = 151# - {...}
199 = 7# - {...} = 11# - {...} = 17# - {...} = 23# - {...} = 67# - {...} = 71# - {...}
211 = 11# - {...} = 13# - {...} = 17# - {...} = 31# - {...} = 107# - {...}
223 = 11# - {...} = 17# - {...} = 61# - {...} = 127# - {...} = 131# - {...} = 179# - {...} = 181# - {...}
227 = 11# - {...} = 13# - {...} = 29# - {...} = 31# - {...} = 41# - {...} = 211# - {...}
229 = 11# - {...} = 19# - {...} = 43# - {...} = 53# - {...}
233 = 67# - {...} = 149# - {...} = 167# - {...}
239 = 17# - {...} = 19# - {...} = 23# - {...} = 37# - {...} = 41# - {...} = 71# - {...} = 79# - {...} = 101# - {...} = 163# - {...}
241 = 11# - {...} = 13# - {...} = 19# - {...} = 29# - {...} = 61# - {...} = 71# - {...}
251 = 31# - {...} = 41# - {...} = 79# - {...} = 97# - {...} = 113# - {...}
257 = 11# - {...} = 17# - {...} = 19# - {...} = 29# - {...} = 31# - {...} = 37# - {...} = 73# - {...} = 97# - {...} = 113# - {...} = 127# - {...} = 167# - {...} = 229# - {...}
263 = 17# - {...} = 37# - {...} = 43# - {...} = 61# - {...} = 71# - {...} = 83# - {...} = 107# - {...} = 109# - {...}
269 = 13# - {...} = 17# - {...} = 23# - {...} = 31# - {...} = 61# - {...}
271 = 11# - {...} = 13# - {...} = 31# - {...} = 59# - {...} = 79# - {...} = 89# - {...}
277 = 13# - {...} = 17# - {...} = 29# - {...} = 47# - {...} = 59# - {...} = 89# - {...} = 113# - {...}
281 = 11# - {...} = 19# - {...} = 37# - {...} = 43# - {...} = 67# - {...} = 113# - {...} = 139# - {...}
283 = 11# - {...} = 17# - {...} = 23# - {...} = 31# - {...} = 37# - {...} = 107# - {...}
293 = 11# - {...} = 17# - {...} = 23# - {...} = 31# - {...} = 43# - {...} = 53# - {...} = 103# - {...} = 191# - {...} = 197# - {...}
用时 0.05720 秒

如果严格一点来说，您一楼的内容不能算作某一猜想，因为随便一个正常人都能举出几个这样的例子来。
您得再加上一个关键条件，如对于所有数（或某类数） 前述条件都能成立才行，或者是符合一楼的内容数有无限多。这样才行。是否这个理儿？

作为猜想也无不可，只是不是独立的猜想，而是哥德巴赫猜想的反向的离散点的表达，因为：
p = P# - q，
即p + q= P# ，颠倒顺序后为P#=p + q
P#是偶数，
P≥5，q>5
p与 q都是素数，
即是偶数=素数+素数，这就是哥德巴赫猜想，但是它不是哥德巴赫猜想的全部，只是其中一些离散点的偶数的表达，且
p = P# - q是偶数R=Pa+Pb的相反的表达方式，故称其为【哥德巴赫猜想的反向的离散点的表达】，这种表达是有限的，因为P#当P较大时是难以计算的。

一个命题，不管真假，其前提条件是不能随便更改的。
如果增加条件，或者修改条件，那便是另外一个命题了。这就是所谓的“跑偏”。

山水先生的考虑是正确的！
本质上说，P#是一类特定的偶数。
p = P# - q，与 P# = p + q，是等价命题。
两个表达式蕴含的意义，本质上都是说： 形如P#的偶数都可以表示为：大于5的两个奇素数之和。
属于哥德巴赫猜想的子命题。

【素阶乘猜想：对于大于5的素数p，存在素数P，q使得p = P# - q】只是哥德巴赫猜想的一部分，因为P#为素数阶乘，中必然存在偶素数2，所以该阶乘必须是偶数，而偶数可以表示为两个奇素数的和的就是哥德巴赫猜想所要表示的。证明了哥德巴赫猜想，就可以推出该结论。反之则不行的。两者是可以同时被证明的。

回复 S云淡风清X：先生应该是高校老师，我明知你在炒剩饭，且找不到不当之处，实在是高。不过学生得不到新的思想启发。还是会有一些失落感的。