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[擂台] 1-9各用若干次,最多可组成多少个素数?

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发表于 2008-10-26 17:35:31 | 显示全部楼层
k=3应该可以达到14,而k=4我觉得应该可以达到17。
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2008-10-26 19:14:01 | 显示全部楼层
同意k = 3的
但为什么说k = 4,是17个呢?
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
 楼主| 发表于 2008-10-27 07:44:32 | 显示全部楼层
这道题是我自编的,
感觉用计算机搜索最大的难点在于设计良好的数据结构和高效的算法。
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2008-10-27 08:33:06 | 显示全部楼层
有10000内素数表足够了
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2008-10-27 08:33:40 | 显示全部楼层
需要找除个位数字外,其他位是2,4,5,6,8的素数
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2008-10-27 08:34:39 | 显示全部楼层
这种数字是
125 * 4 = 500个,
素数应该不多
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2008-10-27 09:37:23 | 显示全部楼层
而且优先使用位数低的数.k=3和k=4完全可以手工构造
k=3我找到了一个14个数的:
2,3,5,7,29,41,47,53,61,67,83,89,541,6829
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2008-10-27 10:12:53 | 显示全部楼层
k=4时18还可以达的到,不过看来要借助一下计算机,共199个解:
2,3,5,7,29,41,43,47,53,59,61,67,83,89,421,661,827,859
2,3,5,7,29,41,43,47,53,59,61,67,83,89,421,661,857,829
2,3,5,7,29,41,43,47,53,59,61,67,83,89,421,661,587,829
2,3,5,7,29,41,43,47,53,59,61,67,83,89,521,641,887,269
2,3,5,7,29,41,43,47,53,59,61,67,83,89,521,661,487,829
2,3,5,7,29,41,43,47,53,59,61,67,83,89,521,881,647,269
2,3,5,7,29,41,43,47,53,59,61,67,83,89,521,881,467,269
2,3,5,7,29,41,43,47,53,59,61,67,83,89,821,821,647,659
2,3,5,7,29,41,43,47,53,59,61,67,83,89,821,821,647,569
2,3,5,7,29,41,43,47,53,59,61,67,83,89,821,821,467,659
2,3,5,7,29,41,43,47,53,59,61,67,83,89,821,821,467,569
2,3,5,7,29,41,43,47,53,59,61,67,83,89,241,661,827,859
2,3,5,7,29,41,43,47,53,59,61,67,83,89,241,661,857,829
2,3,5,7,29,41,43,47,53,59,61,67,83,89,241,661,587,829
2,3,5,7,29,41,43,47,53,59,61,67,83,89,541,661,827,829
2,3,5,7,29,41,43,47,53,59,61,67,83,89,541,661,887,229
2,3,5,7,29,41,43,47,53,59,61,67,83,89,641,821,827,659
2,3,5,7,29,41,43,47,53,59,61,67,83,89,641,821,827,569
2,3,5,7,29,41,43,47,53,59,61,67,83,89,641,821,857,269
2,3,5,7,29,41,43,47,53,59,61,67,83,89,641,821,587,269
2,3,5,7,29,41,43,47,53,59,61,67,83,89,641,881,227,659
2,3,5,7,29,41,43,47,53,59,61,67,83,89,641,881,227,569
2,3,5,7,29,41,43,47,53,59,61,67,83,89,641,881,257,269
2,3,5,7,29,41,43,47,53,59,61,67,83,89,251,641,887,269
2,3,5,7,29,41,43,47,53,59,61,67,83,89,251,461,887,269
2,3,5,7,29,41,43,47,53,59,61,67,83,89,251,661,487,829
2,3,5,7,29,41,43,47,53,59,61,67,83,89,251,881,647,269
2,3,5,7,29,41,43,47,53,59,61,67,83,89,251,881,467,269
2,3,5,7,29,41,43,47,53,59,61,67,83,89,461,521,887,269
2,3,5,7,29,41,43,47,53,59,61,67,83,89,461,821,827,659
2,3,5,7,29,41,43,47,53,59,61,67,83,89,461,821,827,569
2,3,5,7,29,41,43,47,53,59,61,67,83,89,461,821,857,269
2,3,5,7,29,41,43,47,53,59,61,67,83,89,461,821,587,269
2,3,5,7,29,41,43,47,53,59,61,67,83,89,461,881,227,659
2,3,5,7,29,41,43,47,53,59,61,67,83,89,461,881,227,569
2,3,5,7,29,41,43,47,53,59,61,67,83,89,461,881,257,269
2,3,5,7,29,41,43,47,53,59,61,67,83,89,661,821,547,829
2,3,5,7,29,41,43,47,53,59,61,67,83,89,661,821,457,829
2,3,5,7,29,41,43,47,53,59,61,67,83,89,661,881,547,229
2,3,5,7,29,41,43,47,53,59,61,67,83,89,661,881,457,229
2,3,5,7,29,41,43,47,53,59,61,67,83,89,281,821,647,659
2,3,5,7,29,41,43,47,53,59,61,67,83,89,281,821,647,569
2,3,5,7,29,41,43,47,53,59,61,67,83,89,281,821,467,659
2,3,5,7,29,41,43,47,53,59,61,67,83,89,281,821,467,569
2,3,5,7,29,41,43,47,53,59,61,67,83,89,281,641,827,659
2,3,5,7,29,41,43,47,53,59,61,67,83,89,281,641,827,569
2,3,5,7,29,41,43,47,53,59,61,67,83,89,281,641,857,269
2,3,5,7,29,41,43,47,53,59,61,67,83,89,281,641,587,269
2,3,5,7,29,41,43,47,53,59,61,67,83,89,281,461,827,659
2,3,5,7,29,41,43,47,53,59,61,67,83,89,281,461,827,569
2,3,5,7,29,41,43,47,53,59,61,67,83,89,281,461,857,269
2,3,5,7,29,41,43,47,53,59,61,67,83,89,281,461,587,269
2,3,5,7,29,41,43,47,53,59,61,67,83,89,281,661,547,829
2,3,5,7,29,41,43,47,53,59,61,67,83,89,281,661,457,829
2,3,5,7,29,41,43,47,53,59,61,67,83,89,281,281,647,659
2,3,5,7,29,41,43,47,53,59,61,67,83,89,281,281,647,569
2,3,5,7,29,41,43,47,53,59,61,67,83,89,281,281,467,659
2,3,5,7,29,41,43,47,53,59,61,67,83,89,281,281,467,569
2,3,5,7,23,29,41,47,53,59,61,67,83,89,421,641,887,659
2,3,5,7,23,29,41,47,53,59,61,67,83,89,421,641,887,569
2,3,5,7,23,29,41,47,53,59,61,67,83,89,421,461,887,659
2,3,5,7,23,29,41,47,53,59,61,67,83,89,421,461,887,569
2,3,5,7,23,29,41,47,53,59,61,67,83,89,421,661,487,859
2,3,5,7,23,29,41,47,53,59,61,67,83,89,421,881,647,659
2,3,5,7,23,29,41,47,53,59,61,67,83,89,421,881,647,569
2,3,5,7,23,29,41,47,53,59,61,67,83,89,421,881,467,659
2,3,5,7,23,29,41,47,53,59,61,67,83,89,421,881,467,569
2,3,5,7,23,29,41,47,53,59,61,67,83,89,521,661,887,449
2,3,5,7,23,29,41,47,53,59,61,67,83,89,241,641,887,659
2,3,5,7,23,29,41,47,53,59,61,67,83,89,241,641,887,569
2,3,5,7,23,29,41,47,53,59,61,67,83,89,241,461,887,659
2,3,5,7,23,29,41,47,53,59,61,67,83,89,241,461,887,569
2,3,5,7,23,29,41,47,53,59,61,67,83,89,241,661,487,859
2,3,5,7,23,29,41,47,53,59,61,67,83,89,241,881,647,659
2,3,5,7,23,29,41,47,53,59,61,67,83,89,241,881,647,569
2,3,5,7,23,29,41,47,53,59,61,67,83,89,241,881,467,659
2,3,5,7,23,29,41,47,53,59,61,67,83,89,241,881,467,569
2,3,5,7,23,29,41,47,53,59,61,67,83,89,541,641,887,269
2,3,5,7,23,29,41,47,53,59,61,67,83,89,541,661,487,829
2,3,5,7,23,29,41,47,53,59,61,67,83,89,541,881,647,269
2,3,5,7,23,29,41,47,53,59,61,67,83,89,541,881,467,269
2,3,5,7,23,29,41,47,53,59,61,67,83,89,641,821,647,859
2,3,5,7,23,29,41,47,53,59,61,67,83,89,641,821,467,859
2,3,5,7,23,29,41,47,53,59,61,67,83,89,641,821,487,659
2,3,5,7,23,29,41,47,53,59,61,67,83,89,641,821,487,569
2,3,5,7,23,29,41,47,53,59,61,67,83,89,641,641,827,859
2,3,5,7,23,29,41,47,53,59,61,67,83,89,641,641,857,829
2,3,5,7,23,29,41,47,53,59,61,67,83,89,641,641,587,829
2,3,5,7,23,29,41,47,53,59,61,67,83,89,641,881,547,269
2,3,5,7,23,29,41,47,53,59,61,67,83,89,641,881,457,269
2,3,5,7,23,29,41,47,53,59,61,67,83,89,251,661,887,449
2,3,5,7,23,29,41,47,53,59,61,67,83,89,461,821,647,859
2,3,5,7,23,29,41,47,53,59,61,67,83,89,461,821,467,859
2,3,5,7,23,29,41,47,53,59,61,67,83,89,461,821,487,659
2,3,5,7,23,29,41,47,53,59,61,67,83,89,461,821,487,569
2,3,5,7,23,29,41,47,53,59,61,67,83,89,461,541,887,269
2,3,5,7,23,29,41,47,53,59,61,67,83,89,461,641,827,859
2,3,5,7,23,29,41,47,53,59,61,67,83,89,461,641,857,829
2,3,5,7,23,29,41,47,53,59,61,67,83,89,461,641,587,829
2,3,5,7,23,29,41,47,53,59,61,67,83,89,461,461,827,859
2,3,5,7,23,29,41,47,53,59,61,67,83,89,461,461,857,829
2,3,5,7,23,29,41,47,53,59,61,67,83,89,461,461,587,829
2,3,5,7,23,29,41,47,53,59,61,67,83,89,461,881,547,269
2,3,5,7,23,29,41,47,53,59,61,67,83,89,461,881,457,269
2,3,5,7,23,29,41,47,53,59,61,67,83,89,661,821,857,449
2,3,5,7,23,29,41,47,53,59,61,67,83,89,661,821,587,449
2,3,5,7,23,29,41,47,53,59,61,67,83,89,661,881,257,449
2,3,5,7,23,29,41,47,53,59,61,67,83,89,281,641,647,859
2,3,5,7,23,29,41,47,53,59,61,67,83,89,281,641,467,859
2,3,5,7,23,29,41,47,53,59,61,67,83,89,281,641,487,659
2,3,5,7,23,29,41,47,53,59,61,67,83,89,281,641,487,569
2,3,5,7,23,29,41,47,53,59,61,67,83,89,281,461,647,859
2,3,5,7,23,29,41,47,53,59,61,67,83,89,281,461,467,859
2,3,5,7,23,29,41,47,53,59,61,67,83,89,281,461,487,659
2,3,5,7,23,29,41,47,53,59,61,67,83,89,281,461,487,569
2,3,5,7,23,29,41,47,53,59,61,67,83,89,281,661,857,449
2,3,5,7,23,29,41,47,53,59,61,67,83,89,281,661,587,449
2,3,5,7,23,29,41,43,47,59,61,67,83,89,421,661,857,859
2,3,5,7,23,29,41,43,47,59,61,67,83,89,421,661,587,859
2,3,5,7,23,29,41,43,47,59,61,67,83,89,521,641,887,659
2,3,5,7,23,29,41,43,47,59,61,67,83,89,521,641,887,569
2,3,5,7,23,29,41,43,47,59,61,67,83,89,521,661,487,859
2,3,5,7,23,29,41,43,47,59,61,67,83,89,521,881,647,659
2,3,5,7,23,29,41,43,47,59,61,67,83,89,521,881,647,569
2,3,5,7,23,29,41,43,47,59,61,67,83,89,521,881,467,659
2,3,5,7,23,29,41,43,47,59,61,67,83,89,521,881,467,569
2,3,5,7,23,29,41,43,47,59,61,67,83,89,241,661,857,859
2,3,5,7,23,29,41,43,47,59,61,67,83,89,241,661,587,859
2,3,5,7,23,29,41,43,47,59,61,67,83,89,541,661,827,859
2,3,5,7,23,29,41,43,47,59,61,67,83,89,541,661,857,829
2,3,5,7,23,29,41,43,47,59,61,67,83,89,541,661,587,829
2,3,5,7,23,29,41,43,47,59,61,67,83,89,641,821,857,659
2,3,5,7,23,29,41,43,47,59,61,67,83,89,641,821,857,569
2,3,5,7,23,29,41,43,47,59,61,67,83,89,641,821,587,659
2,3,5,7,23,29,41,43,47,59,61,67,83,89,641,821,587,569
2,3,5,7,23,29,41,43,47,59,61,67,83,89,641,881,257,659
2,3,5,7,23,29,41,43,47,59,61,67,83,89,641,881,257,569
2,3,5,7,23,29,41,43,47,59,61,67,83,89,641,881,557,269
2,3,5,7,23,29,41,43,47,59,61,67,83,89,251,641,887,659
2,3,5,7,23,29,41,43,47,59,61,67,83,89,251,641,887,569
2,3,5,7,23,29,41,43,47,59,61,67,83,89,251,461,887,659
2,3,5,7,23,29,41,43,47,59,61,67,83,89,251,461,887,569
2,3,5,7,23,29,41,43,47,59,61,67,83,89,251,661,487,859
2,3,5,7,23,29,41,43,47,59,61,67,83,89,251,881,647,659
2,3,5,7,23,29,41,43,47,59,61,67,83,89,251,881,647,569
2,3,5,7,23,29,41,43,47,59,61,67,83,89,251,881,467,659
2,3,5,7,23,29,41,43,47,59,61,67,83,89,251,881,467,569
2,3,5,7,23,29,41,43,47,59,61,67,83,89,461,521,887,659
2,3,5,7,23,29,41,43,47,59,61,67,83,89,461,521,887,569
2,3,5,7,23,29,41,43,47,59,61,67,83,89,461,821,857,659
2,3,5,7,23,29,41,43,47,59,61,67,83,89,461,821,857,569
2,3,5,7,23,29,41,43,47,59,61,67,83,89,461,821,587,659
2,3,5,7,23,29,41,43,47,59,61,67,83,89,461,821,587,569
2,3,5,7,23,29,41,43,47,59,61,67,83,89,461,881,257,659
2,3,5,7,23,29,41,43,47,59,61,67,83,89,461,881,257,569
2,3,5,7,23,29,41,43,47,59,61,67,83,89,461,881,557,269
2,3,5,7,23,29,41,43,47,59,61,67,83,89,661,821,547,859
2,3,5,7,23,29,41,43,47,59,61,67,83,89,661,821,457,859
2,3,5,7,23,29,41,43,47,59,61,67,83,89,281,641,857,659
2,3,5,7,23,29,41,43,47,59,61,67,83,89,281,641,857,569
2,3,5,7,23,29,41,43,47,59,61,67,83,89,281,641,587,659
2,3,5,7,23,29,41,43,47,59,61,67,83,89,281,641,587,569
2,3,5,7,23,29,41,43,47,59,61,67,83,89,281,461,857,659
2,3,5,7,23,29,41,43,47,59,61,67,83,89,281,461,857,569
2,3,5,7,23,29,41,43,47,59,61,67,83,89,281,461,587,659
2,3,5,7,23,29,41,43,47,59,61,67,83,89,281,461,587,569
2,3,5,7,23,29,41,43,47,59,61,67,83,89,281,661,547,859
2,3,5,7,23,29,41,43,47,59,61,67,83,89,281,661,457,859
2,3,5,7,23,29,41,43,47,53,59,61,67,89,421,661,887,859
2,3,5,7,23,29,41,43,47,53,59,61,67,89,821,881,647,659
2,3,5,7,23,29,41,43,47,53,59,61,67,89,821,881,647,569
2,3,5,7,23,29,41,43,47,53,59,61,67,89,821,881,467,659
2,3,5,7,23,29,41,43,47,53,59,61,67,89,821,881,467,569
2,3,5,7,23,29,41,43,47,53,59,61,67,89,241,661,887,859
2,3,5,7,23,29,41,43,47,53,59,61,67,89,541,661,887,829
2,3,5,7,23,29,41,43,47,53,59,61,67,89,641,821,887,659
2,3,5,7,23,29,41,43,47,53,59,61,67,89,641,821,887,569
2,3,5,7,23,29,41,43,47,53,59,61,67,89,641,881,827,659
2,3,5,7,23,29,41,43,47,53,59,61,67,89,641,881,827,569
2,3,5,7,23,29,41,43,47,53,59,61,67,89,641,881,857,269
2,3,5,7,23,29,41,43,47,53,59,61,67,89,641,881,587,269
2,3,5,7,23,29,41,43,47,53,59,61,67,89,461,821,887,659
2,3,5,7,23,29,41,43,47,53,59,61,67,89,461,821,887,569
2,3,5,7,23,29,41,43,47,53,59,61,67,89,461,881,827,659
2,3,5,7,23,29,41,43,47,53,59,61,67,89,461,881,827,569
2,3,5,7,23,29,41,43,47,53,59,61,67,89,461,881,857,269
2,3,5,7,23,29,41,43,47,53,59,61,67,89,461,881,587,269
2,3,5,7,23,29,41,43,47,53,59,61,67,89,661,821,487,859
2,3,5,7,23,29,41,43,47,53,59,61,67,89,661,881,547,829
2,3,5,7,23,29,41,43,47,53,59,61,67,89,661,881,457,829
2,3,5,7,23,29,41,43,47,53,59,61,67,89,281,641,887,659
2,3,5,7,23,29,41,43,47,53,59,61,67,89,281,641,887,569
2,3,5,7,23,29,41,43,47,53,59,61,67,89,281,461,887,659
2,3,5,7,23,29,41,43,47,53,59,61,67,89,281,461,887,569
2,3,5,7,23,29,41,43,47,53,59,61,67,89,281,661,487,859
2,3,5,7,23,29,41,43,47,53,59,61,67,89,281,881,647,659
2,3,5,7,23,29,41,43,47,53,59,61,67,89,281,881,647,569
2,3,5,7,23,29,41,43,47,53,59,61,67,89,281,881,467,659
2,3,5,7,23,29,41,43,47,53,59,61,67,89,281,881,467,569
Total 199 solutions

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毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2008-10-27 14:02:17 | 显示全部楼层
大k值是否能通过小k值生成结果
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2021-9-10 07:24:10 | 显示全部楼层
本帖最后由 数论爱好者 于 2021-9-10 10:02 编辑

换个思路研究一下,组合数学我不行
在给定范围内,组成的所有素数,去掉含0组成的素数,剩下的素数全部是由1-9组成的素数,1-9重复的次数各不相同.
在x=10^2,有25个素数,25个素数都没有0出现,所以1-9组成的素数有25个
在x=10^3,有168个素数,有15个含0组成的素数,所以1-9组成的不含0素数有168-15=153个
在x=10^5,有9592个素数,由excel2007统计9592个素数:查找全部0,共计2470个单元格被找到,一个单元格代表一个素数.
所以10^5以内,共有含0素数=2470个
含1素数=4917个
含2素数=3357个
含3素数=4877个
含4素数=3231个
含5素数=3282个
含6素数=3225个
含7素数=4819个
含8素数=3217个
含9素数=4826个
含0素数最少
在10^5以内,由1-9组成的不含0素数有9592-2470=7122个
那么在x=10^12以内,含0素数有多少个?

毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
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