문제1500--Prime Gap

### 1500: Prime Gap

실행시간 제한: 5 Sec  메모리사용 제한: 64 MB
제출: 83  통과: 51
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#### 문제 설명

The sequence of n − 1 consecutive composite numbers (positive integers that are not prime and not equal to 1) lying between two successive prime numbers p and p + n is called a prime gap of length n. For example, ‹24, 25, 26, 27, 28› between 23 and 29 is a prime gap of length 6.

Your mission is to write a program to calculate, for a given positive integer k, the length of the prime gap that contains k. For convenience, the length is considered 0 in case no prime gap contains k.

#### 입력 설명

The input is a sequence of lines each of which contains a single positive integer. Each positive integer is greater than 1 and less than or equal to the 100000th prime number, which is 1299709. The end of the input is indicated by a line containing a single zero.

#### 출력 설명

The output should be composed of lines each of which contains a single non-negative integer. It is the length of the prime gap that contains the corresponding positive integer in the input if it is a composite number, or 0 otherwise. No other characters should occur in the output.

#### 입력 예시 Copy

10
11
27
2
492170
0

#### 출력 예시 Copy

4
0
6
0
114