✔ 最佳答案
1a)All prime numbers which is > 2 , can be written as 2n + 1(n > 0)
Case 1 :When the smaller one is 2 , 2 + 0 = 3 : are two consecutive prime numbers with the difference 0.
Case 2 :Let the smaller one is 2n + 1 (n>0),
For difference 3 : 2n + 1 + 3 = 2n + 4 = 2(n + 2) is not prime number.
For difference 5 : 2n + 1 + 5 = 2n + 6 = 2(n + 3) is not prime number.
For difference 7 : 2n + 1 + 7 = 2n + 8 = 2(n + 4) is not prime number.
So 3 , 5 , 7 cannot be the difference between two consecutive prime numbers.
1b) For difference 2 :
3 + 2 = 5
5 + 2 = 7
For difference 4 :
13 + 4 = 17
19 + 4 = 23 etc.
For difference 6 :
23 + 6 = 29
31 + 6 = 37
2009-10-13 17:11:20 補充:
001 好人 :
Your answer :
Difference = 3
Example: 2 and 5
But 2 and 5 is not two 『consecutive』 primes !
2009-10-13 17:32:16 補充:
Case 1 :When the smaller one is 2 , 2 + 1 = 3 : are two consecutive prime numbers with the difference 1.