试题与答案

已知p，p+2，p+6，p+8，p+14都是质数，则这样的质数p共有______

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题型：填空题

题目：

已知p，p+2，p+6，p+8，p+14都是质数，则这样的质数p共有______个．

答案：

显然，p=2和p=3不符合要求．

p=5时，容易看出5，7，11，13，19都是质数，

p＞5时，按p除以5的余数分类：

p=5n时，p不是质数；

p=5n+1时，p+14=5（n+3）不是质数；

p=5n+2时，p+8=5（n+2）不是质数；

p=5n+3时，p+2=5（n+1）不是质数；

p=5n+4时，p+6=5（n+2）不是质数．

因此，只有p=5一个．

故答案为：1．

考点：有理数定义及分类
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