設n是自然數，如果n、n+2、n+4都是質數，n是甚麼?

mod(n＋4, 3) = mod(n＋1, 3)
Since one of mod(n, 3), mod(n＋1, 3), mod(n＋2, 3) must be 0, therefore, exactly one of the numbers n, n＋2, n＋4 must be divisible by 3. If any of these number is bigger than 3 then it is not prime.
Therefore the only possible value for n is 3.

2008-03-18 21:57:47 補充：
只是不同的寫法吧
如果你明白 3 = 1 (mod 2)，
那1 = mod(3, 2)是表達同樣的意思。

我不知道這是不是standard的寫法，但一般人都會這樣寫，尤其是讀computer science的比較習慣prefix notation。而且一般的理解mod(a, b)的數值都會選0<=mod(a,b)

Consider n mod 3
(1) n = 1 (mod 3)
n+2 = 0(mod)3
n&gt;=4
n+2 &gt;=6
so no solution
(2) n = 2 (mod 3)
n+4 = 0 (mod 3)
n&gt;=2
n+4&gt;=6
so no solution
(3) n =0 (mod 3)
so n =3
n=3 ,n+2=5 ,n+4=7
So n =3