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)

# Primality test
import numpy as np

n = 100003 # limit

primes = np.ones((n + 1,), dtype=int)
primes[0] = 0
primes[1] = 0
primes[2*2::2] = 0
primes[3*2::3] = 0
m = 5
l = n ** 0.5
while m <= l:
    if primes[m]:
        primes[m * 2::m] = 0
    if m % 6 == 5:
        m += 2
    else:
        m += 4

# solve
X = int(input())

while True:
    if primes[X]:
        print(X)
        break
    X += 1