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最小素因子不超过Pm的合数链长度最大值

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猜想:
最小素因子不超过 p_m 的合数链长度最大值是:D_max ≤ 2 p_(m+1)
.
两个实例
实例1: p_m = 37,D_max = 66
最小素因子不超过37的合数链长度为D_max = 66 = p_m + p_(m-2) = 37 + 29
187219155 599,187219155 601,187219155 607,187219155 611,187219155 613
187219155 617,187219155 619,187219155 623,187219155 629,187219155 631
187219155 637,187219155 641,187219155 643,187219155 647,187219155 649
187219155 653
.
参照基准值 Z_o = 1872 19155 600
- (1_7), Z_o + (1_23, 7_11, 11_19, 13_7, 17_13, 19_17,
23_37, 29_11, 31_31, 37_29, 41_7, 43_13, 47_23, 49_19, 53_17)
符号意义:43_13 表示 13 | (Z_o + 43)
.
敬请电算大师验证,或者给出反例。


IP属地:上海1楼2025-04-29 08:02回复
    实例2: p_m = 43,D_max = 90
    最小素因子不超过43的合数链长度为D_max = 90 = p_m + p_(m+1) = 43 + 47
    区间 (1447829244 3583, 14478 29244 3673)内的89个连续自然数,最小素因子都不超过43.
    最小素因子大于等于7的奇合数序列的最小素因子排列结构是:
    - (7,13,11,31), Z_o,+ (7,23,19,17,29,43, 37,7,41,11,13,7,17,19,23,11,31,13,7)
    参照基准值 Z_o = 14478 29244 3600
    -(17_ , 13_7, 11_13, 7_11, 1_31 ), Z_o, + (1_7, 7_23, 11_19, 13_17, 17_29, 19_43 ,
    23_37, 29_7, 31_41, 37_11 ,41_13, 43_7, 47_17, 49_19, 53_23, 59_11, 61_31
    67_13, 71_7, 73_ )
    .
    符号意义:43_7 表示 7 | (Z_o + 43)


    IP属地:上海2楼2025-04-29 10:21
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