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)

# coding: utf-8
# submission # - User: herp_sy
# https://atcoder.jp/contests/
#
# lang: Python3 (3.4.3)

import math
import statistics
import numpy as np
import queue

def eratosthenes(n):
  prime = []
  limit = math.sqrt(n)
  data = [i + 1 for i in range(1, n)]
  while True:
    p = data[0]
    if limit <= p:
      return prime + data
    prime.append(p)
    data = [e for e in data if e % p != 0]
  return prime

x = int(input())
while True:
  ary = eratosthenes(x)
  if ary[-1] == x:
    break
  else:
    x += 1
print(x)