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# [讨论] 素阶乘猜想：p = P# - q

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楼主| 发表于 2024-3-23 13:52:17 | 显示全部楼层
 2024-03-23 13:49:22 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# - {...} 307  = 11# - {...} = 13# - {...} = 17# - {...} = 29# - {...} = 37# - {...} = 61# - {...} = 233# - {...} = 263# - {...} 311  = 11# - {...} = 17# - {...} = 23# - {...} = 37# - {...} = 67# - {...} = 97# - {...} = 223# - {...} 313  = 11# - {...} = 13# - {...} = 19# - {...} = 29# - {...} = 41# - {...} = 47# - {...} = 61# - {...} = 67# - {...} = 73# - {...} = 109# - {...} = 223# - {...} = 229# - {...} = 23 9# - {...} 317  = 11# - {...} = 181# - {...} = 257# - {...} = 277# - {...} 331  = 11# - {...} = 17# - {...} = 19# - {...} = 47# - {...} = 53# - {...} = 67# - {...} = 79# - {...} = 311# - {...} 337  = 11# - {...} = 29# - {...} = 53# - {...} = 97# - {...} 347  = 13# - {...} = 29# - {...} = 43# - {...} = 71# - {...} = 211# - {...} = 251# - {...} 349  = 19# - {...} = 37# - {...} = 41# - {...} = 43# - {...} = 223# - {...} = 239# - {...} 353  = 17# - {...} = 23# - {...} = 29# - {...} = 31# - {...} = 41# - {...} = 73# - {...} = 83# - {...} 359  = 11# - {...} = 13# - {...} = 19# - {...} = 113# - {...} 367  = 13# - {...} = 19# - {...} = 29# - {...} = 47# - {...} = 181# - {...} = 263# - {...} = 337# - {...} 373  = 17# - {...} = 23# - {...} = 37# - {...} = 61# - {...} = 67# - {...} = 109# - {...} = 127# - {...} = 139# - {...} = 149# - {...} = 227# - {...} = 367# - {...} 379  = 11# - {...} = 43# - {...} = 61# - {...} = 109# - {...} = 313# - {...} 383  = 17# - {...} = 41# - {...} = 73# - {...} = 79# - {...} = 109# - {...} = 179# - {...} = 239# - {...} = 263# - {...} 389  = 13# - {...} = 17# - {...} = 23# - {...} = 47# - {...} = 67# - {...} = 79# - {...} = 103# - {...} = 137# - {...} 397  = 11# - {...} = 13# - {...} = 31# - {...} = 53# - {...} = 61# - {...} = 73# - {...} = 109# - {...} = 131# - {...} = 367# - {...} 401  = 13# - {...} = 19# - {...} = 23# - {...} = 41# - {...} = 197# - {...} = 337# - {...} 409  = 11# - {...} = 17# - {...} = 47# - {...} = 59# - {...} = 163# - {...} = 173# - {...} = 337# - {...} 419  = 13# - {...} = 29# - {...} = 41# - {...} = 61# - {...} = 67# - {...} = 131# - {...} = 139# - {...} 421  = 11# - {...} = 17# - {...} = 29# - {...} = 73# - {...} = 89# - {...} = 139# - {...} 431  = 11# - {...} = 13# - {...} = 17# - {...} = 29# - {...} = 37# - {...} = 43# - {...} = 59# - {...} = 79# - {...} = 109# - {...} = 163# - {...} = 281# - {...} = 337# - {...} 433  = 11# - {...} = 17# - {...} = 173# - {...} = 431# - {...} 439  = 11# - {...} = 19# - {...} = 23# - {...} = 31# - {...} = 37# - {...} = 113# - {...} = 163# - {...} = 167# - {...} = 229# - {...} = 419# - {...} 443  = 11# - {...} = 13# - {...} = 17# - {...} = 29# - {...} = 83# - {...} = 131# - {...} = 163# - {...} = 233# - {...} = 353# - {...} = 367# - {...} = 397# - {...} 449  = 11# - {...} = 13# - {...} = 17# - {...} = 31# - {...} = 37# - {...} = 103# - {...} = 137# - {...} = 197# - {...} = 331# - {...} = 349# - {...} = 401# - {...} 457  = 13# - {...} = 19# - {...} = 41# - {...} = 47# - {...} = 109# - {...} = 199# - {...} = 349# - {...} 461  = 13# - {...} = 17# - {...} = 31# - {...} = 47# - {...} = 59# - {...} = 101# - {...} = 311# - {...} = 313# - {...} 463  = 11# - {...} = 13# - {...} = 17# - {...} = 47# - {...} = 61# - {...} = 101# - {...} = 151# - {...} = 199# - {...} = 281# - {...} = 367# - {...} = 419# - {...} 467  = 29# - {...} = 37# - {...} = 43# - {...} = 109# - {...} = 271# - {...} = 373# - {...} 479  = 11# - {...} = 17# - {...} = 19# - {...} = 37# - {...} = 53# - {...} = 59# - {...} = 157# - {...} = 233# - {...} = 283# - {...} 487  = 11# - {...} = 19# - {...} = 71# - {...} = 163# - {...} 491  = 19# - {...} = 41# - {...} = 101# - {...} = 113# - {...} = 149# - {...} = 157# - {...} = 239# - {...} 499  = 11# - {...} = 13# - {...} = 19# - {...} = 103# - {...} = 139# - {...} = 157# - {...} = 163# - {...} = 359# - {...} 用时 0.25401 秒 其中7、11、13、17为满解，即可行解全部是有效解；且只有7、11、31少于3个解。

### 点评

 xbtianlang 发表于 2024-3-23 13:52 2024-03-23 13:49:22 7  = 5# - {...} 11  = 5# - {...} = 7# - {...} 一切皆有可能！

 p<10000的唯2解： 11        2        {5,7}

 p<10000的3个解组合： 13        3        {5,7,11} 19        3        {5,7,13} 23        3        {5,11,19} 29        3        {7,11,17} 37        3        {7,11,19} 61        3        {7,17,23} 233        3        {67,149,167} 3191        3        {13,211,2069} 8161        3        {61,373,3607}复制代码

 p<10000的4个解组合： 17        4        {5,7,11,13} 41        4        {11,13,19,29} 43        4        {7,11,19,23} 53        4        {7,17,19,41} 67        4        {11,19,29,47} 71        4        {7,11,13,41} 79        4        {7,19,23,31} 83        4        {7,13,31,79} 109        4        {7,13,17,59} 157        4        {7,11,13,19} 229        4        {11,19,43,53} 317        4        {11,181,257,277} 337        4        {11,29,53,97} 359        4        {11,13,19,113} 433        4        {11,17,173,431} 487        4        {11,19,71,163} 1091        4        {37,83,137,619} 2113        4        {11,13,89,1321} 2129        4        {11,13,37,1439} 2677        4        {23,53,137,617} 3769        4        {13,19,97,383} 4099        4        {13,67,439,661} 7001        4        {13,769,1741,3271} 8353        4        {19,43,59,101}复制代码

 p=36263 ,5个解：{3853, 5197, 5209, 6247, 6397}

 p<10000 唯一解： 7        1        {5} 31        1        {7}

楼主| 发表于 2024-3-26 10:00:57 | 显示全部楼层
 northwolves 发表于 2024-3-24 13:58 p=36263 ,5个解：{3853, 5197, 5209, 6247, 6397} 2024-03-24 16:37:54 ... ... -3846-36241 -3847-36251 36263 {3853, 5197, 5209, 6247, 6397, 6827, 11681} 用时 23836.19552 秒 检验到36251#，用时很长。

### 点评

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