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
题目大意：性感素数是指形如 (p, p+6) 这样的一对素数。给定一个整数，判断其是否为一个性感素数。若N是一个性感素数，则在一行中输出Yes，并在第二行输出与N配对的另一个性感素数（若这样的数不唯一，输出较小的那个）。若N不是性感素数，则在一行中输出No，然后在第二行输出大于N的最小性感素数。
分析：is_prime判断是否为素数。判断p和p-6、p和p+6是否同时为素数，如果是，则为性感素数输出Yes。不是的话就从p+1往后找到第一个满足要求的数ans~
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#include <iostream> #include <cmath> using namespace std; int p, ans; int is_prime(int x) { if (x < 2) return 0; for (int i = 2; i <= sqrt(x); i++) if (x % i == 0) return 0; return 1; } int main() { cin >> p; if (is_prime(p) && is_prime(p - 6)) { cout << "Yes\n" << p - 6; } else if (is_prime(p) && is_prime(p + 6)) { cout << "Yes\n" << p + 6; } else { for (ans = p + 1; ; ans++) { if (is_prime(ans) && is_prime(ans - 6)) break; if (is_prime(ans) && is_prime(ans + 6)) break; } cout << "No\n" << ans; } return 0; } |
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