回复：合数猜想收集贴

最小素因子不超过71的【连续合数链】的排列结构如下：
-(19_Pn 17_31 13_7 11_13 7_11 1_61 ), Z_o, (1_7 7_23 11_17 13_19 17_37 19_29 23_43 29_7 )(31_q1 37_11 41_13 43_7 47_q2 49_q3 53_23 59_11 )(61_q4 67_13 71_7 73_q5 77_29 79_17 83_7 89_19)(91_37 97_7 101_q6 103_11 107_31 109_43 113_7 119_13 121_61 127_7 131_Pn+1)
.
q_i = {41,47,53,59,67,71}

根据19楼构造的，最小素因子不超过71的【连续合数链】结构形式，
可建立下列一次同余式组：
Zo≡0(mod30), Zo≡ -1(mod7), Zo≡ 7(mod11)
Zo≡11(mod13), Zo≡ -11(mod17), Zo≡ -13(mod19)
Zo≡ -7(mod23), Zo≡ -19(mod29), Zo≡ 17(mod31)
Zo≡ - 17(mod37), Zo≡ -23(mod43), Zo≡ 1(mod61)
.
Zo≡ -31(modq_1), Zo≡ -47(modq_2), Zo≡ -49(modq_3)
Zo≡ -61(modq_4), Zo≡ -73(modq_5), Zo≡ -101(modq_6)
.
q_i = {41,47,53,59,67,71}
.
按照孙子定理，设素数连乘积 M=2*3*5*...*71，在区间（0，M）内，存在 1*2*3*4*5*6=720 组最小素因子不超过71的【连续合数链】。

孪生素数合数链猜想：
若p_m,p_(m+1)是孪生素数，即p_(m+1)=p_m + 2，则最小素因子不超过p_m的合数链的最大长度为2 p_(m-1) - 1。

最小素因子不超过29的最长合数链为：
2025-11-29 10:18:03
(6052606537, 6052606583)-------------- 45
6052606537 [67, 151, 598261]
6052606539 [3, 7, 743, 387913]
6052606541 [19, 409, 778871]
6052606543 [17, 997, 357107]
6052606545 [3, 5, 173, 503, 4637]
6052606547 [13, 465585119]
6052606549 [11, 550236959]
6052606551 [3, 167, 1342339]
6052606553 [7, 864658079]
6052606555 [5, 227, 881, 6053]
6052606557 [3, 37, 54527987]
6052606559 [29, 208710571]
6052606561 [23, 47, 5599081]
6052606563 [3, 31, 6827, 9533]
6052606565 [5, 911, 1328783]
6052606567 [7, 79, 1563577]
6052606569 [3, 672511841]
6052606571 [11, 1009, 545329]
6052606573 [13, 1663, 279967]
6052606575 [3, 5, 80701421]
6052606577 [17, 821, 433661]
6052606579 [19, 318558241]
6052606581 [3, 7, 288219361]
6052606583 [6052606583]
(6886779877, 6886779923)-------------- 45
6886779877 [40427, 170351]
6886779879 [3, 7, 53, 6187583]
6886779881 [19, 41, 139, 63601]
6886779883 [17, 223, 1816613]
6886779885 [3, 5, 461, 331973]
6886779887 [13, 421, 1258319]
6886779889 [11, 2377, 263387]
6886779891 [3, 61, 79, 476363]
6886779893 [7, 1511, 651109]
6886779895 [5, 1377355979]
6886779897 [3, 59, 38908361]
6886779899 [23, 1373, 218081]
6886779901 [29, 167, 1422007]
6886779903 [3, 107, 109, 65609]
6886779905 [5, 15391, 89491]
6886779907 [7, 97, 773, 13121]
6886779909 [3, 131, 3203, 5471]
6886779911 [11, 626070901]
6886779913 [13, 257, 12197]
6886779915 [3, 5, 113, 1249, 3253]
6886779917 [17, 405104701]
6886779919 [19, 37, 9796273]
6886779921 [3, 7, 31, 167917]
6886779923 [73, 103, 915917]
用时 882.29762 秒

根据题设：等差数列 x^2, (x+a)^2, (x+b)^2
存在等差中项
(x+a)^2 = [x^2+(x+b)^2]/2 = [2x^2+2bx+b^2]/2
x^2 + 2ax + a^2 = x^2 + bx + (b^2)/2
4ax + 2a^2 = 2bx + b^2
x = (b^2 - 2a^2) / 2(2a - b)
试值法：
a=6，b=10，x=7