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: Accepted)

x = int(input())
p = [True] * 100004
p[0] = False
p[1] = False
for i in range(int(100003 ** 0.5)):
    if p[i] == False:
        continue
    for j in range(2, 100003 // i + 1):
        p[i * j] = False
for i in range(x, 100004):
    if p[i] == True:
        print(i)
        break