7-1 Sexy Primes (20分)

7-1 Sexy Primes (20分)

Sexy primes are pairs of primes of the form (p, p+6), so-named since “sex” is the Latin word for “six”. (Quoted from http://mathworld.wolfram.com/SexyPrimes.html)

Now given an integer, you are supposed to tell if it is a sexy prime.

Input Specification:

Each input file contains one test case. Each case gives a positive integer N (≤10⁸).

Output Specification:

For each case, print in a line Yes if N is a sexy prime, then print in the next line the other sexy prime paired with N (if the answer is not unique, output the smaller number). Or if N is not a sexy prime, print No instead, then print in the next line the smallest sexy prime which is larger than N.

Sample Input 1:

47

Sample Output 1:

Yes
41

Sample Input 2:

21

Sample Output 2:

No
23

思路：
按照题目要求，如果给出的num是素数。且num - 6也是素数，则输出Yes，并输出num - 6；或者num + 6也是素数，则输出Yes，并输出num + 6。如果不满足上述条件，则让num自增，直至满足其一。需要注意的是，小于等于1的都不是素数。

#include
using namespace std;
bool isPrime(int num) {
	if (num <= 1) {
		return false;
	}
	for (int i = 2; i * i <= num; i++) {
		if (num % i == 0) {
			return false;
		}
	}
	return true;
}
int main() {
	int num;
	cin >> num;
	bool sexy = false;
	if (isPrime(num)) {
		if (isPrime(num - 6)) {
			sexy = true;
			printf("Yes\n%d\n", num - 6);
		}
		else if (isPrime(num + 6)) {
			sexy = true;
			printf("Yes\n%d\n", num + 6);
		}
	}
	if (!sexy) {
		while (true) {
			while (!isPrime(num)) {
				++num;
			}
			if (isPrime(num - 6) || isPrime(num + 6)) {
				break;
			}
			else ++num;
		}
		printf("No\n%d\n", num);
	}
}