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发表于 2021-7-23 10:29
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蔡家雄 发表于 2021-7-23 08:09
若 k=0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15 时,
则 23025749 + 60*(4^k - 1)/(4 - 1) 均为素数。
若 k=0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15 时,
则 23025749 + 60*(4^k - 1)/(4 - 1) 均为素数。
令F=23025749 + 60*(4^k - 1)/(4 - 1)
k 4^k-1 F 分解式
0 0 23025749 23025749 is prime
1 3 23025809 23025809 is prime
2 15 23026109 23026109=17*83*16319
3 63 23027369 23027369=349*65981
4 255 23032469 23032469 is prime
5 1023 23052929 23052929 is prime
6 4095 23134829 23134829=113*204733
7 16383 23462489 23462489 is prime
8 65535 24773189 24773189=7*3539027
9 262143 30016049 30016049=7*1153*3719
10 1048575 50987549 50987549 is prime
11 4194303 134873609 134873609=13*19*546047
12 16777215 470417909 470417909=13*61*593213
13 67108863 1812595169 1812595169=7*11*23540197
14 268435455 7181304269 7181304269=419*547*31333
15 1073741823 28656140729 28656140729=17*73*2371*9739
其中素数只有6个,对应的k等于0,1,4,5,7,10。其余都是合数,命题不成立!
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