2與3也是質數呀
可是並非 6的倍數加減1
所以,應該修正成
除了2與3之外,質數都是6的倍數加減1
證明如下:
正整數可分為以下六類
(1)6K+1
(2)6K+2
(3)6K+3
(4)6K+4
(5)6K+5
(6)6K+6
其中K為非負整數
(1)6K+1
(2)6K+2=2(3K+1)
(3)6K+3=3(2K+1)
(4)6K+4=2(3K+2)
(5)6K+5
(6)6K+6=6(K+1)
當K=0時,有質數2,3,5
當K>=1時,只剩6K+1與6K+5有機會為質數(其他都可被分解)
故得證
On 10月19日, 下午10時40分, ksjeng <ksj...@tp.edu.tw> wrote:
> 1 = 6 * 0 + 1
> 2
> 3
> 5 = 6 * 1 - 1
> 7 = 6 * 1 + 1
> 11 = 6 * 2 - 1
> 13 = 6 * 2 + 1
> 17 = 6 * 3 - 1
> 19 = 6 * 3 + 1
> 23 = 6 * 4 - 1
> 29 = 6 * 5 - 1
> 31 = 6 * 5 + 1
> 37 = 6 * 6 + 1
> 41 = 6 * 7 - 1
> 43 = 6 * 7 + 1
> 47 = 6 * 8 - 1
> 53 = 6 * 9 - 1
> 59 = 6 * 10 - 1
> 61 = 6 * 10 + 1
> 67 = 6 * 11 + 1
> 71 = 6 * 12 - 1
> 73 = 6 * 12 + 1
> 79 = 6 * 13 + 1
> 83 = 6 * 14 - 1
> 89 = 6 * 15 - 1
> 97 = 6 * 16 + 1
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