Problem:
Score: 300 points

Problem Statement

Find the minimum prime number greater than or equal to X.

Notes

A prime number is an integer greater than 1 that cannot be evenly divided by any positive integer except 1 and itself.

For example, 2, 3, and 5 are prime numbers, while 4 and 6 are not.

Constraints

2 \le X \le 10^5

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X

Output

Print the minimum prime number greater than or equal to X.

Sample Input 1

20

Sample Output 1

23

The minimum prime number greater than or equal to 20 is 23.

Sample Input 2

2

Sample Output 2

2

X itself can be a prime number.

Sample Input 3

99992

Sample Output 3

100003

Solution in Python (3.4.3) (judge verdict: Wrong Answer)

import math

X = int(input())

def prime(x):
    if x >=3:
        if x % 2 == 0:
            return False
        else:    
            T = True
            i = 2
            while (T == True)&(1 < i <= math.ceil(math.sqrt(x))):
                if x % i == 0:
                    T = False
                i +=1
            return T
    else:
        return True

if X % 2 == 0:
    T = X + 1
    while (prime(T) == False):
        T +=2
    print(T)
else:
    T = X
    while (prime(T) == False):
        T +=2
    print(T)