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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.*;
import java.util.*;

public class Main {
  public static void main(String[] args) {
    FastScanner fs = new FastScanner();
    int X = fs.nextInt();
    while (!isPrime(X)) X++;
    System.out.println(X); 
  }

  public static boolean isPrime(int n) {
    if(n < 2) return false;
    if(n == 2) return true;
    if(n % 2 == 0) return false;
    for(int i = 3; i * i <= n; i += 2) {
      if(n % i == 0) return false;
    }
    return true;
  }
}

class FastScanner {
  private final InputStream in = System.in;
  private final byte[] buffer = new byte[1024];
  private int ptr = 0;
  private int buflen = 0;

  private boolean hasNextByte() {
    if (ptr < buflen) {
      return true;
    } else {
      ptr = 0;
      try {
        buflen = in.read(buffer);
      } catch (IOException e) {
        e.printStackTrace();
      }
      if (buflen <= 0) {
        return false;
      }
    }
    return true;
  }

  private int readByte() {
    if (hasNextByte())
    return buffer[ptr++];
    else
    return -1;
  }

  private static boolean isPrintableChar(int c) {
    return 33 <= c && c <= 126;
  }

  public boolean hasNext() {
    while (hasNextByte() && !isPrintableChar(buffer[ptr]))
    ptr++;
    return hasNextByte();
  }

  public String next() {
    if (!hasNext())
    throw new NoSuchElementException();
    StringBuilder sb = new StringBuilder();
    int b = readByte();
    while (isPrintableChar(b)) {
      sb.appendCodePoint(b);
      b = readByte();
    }
    return sb.toString();
  }

  public long nextLong() {
    if (!hasNext())
    throw new NoSuchElementException();
    long n = 0;
    boolean minus = false;
    int b = readByte();
    if (b == '-') {
      minus = true;
      b = readByte();
    }
    if (b < '0' || '9' < b) {
      throw new NumberFormatException();
    }
    while (true) {
      if ('0' <= b && b <= '9') {
        n *= 10;
        n += b - '0';
      } else if (b == -1 || !isPrintableChar(b)) {
        return minus ? -n : n;
      } else {
      throw new NumberFormatException();
      }
      b = readByte();
    }
  }

  public int nextInt() {
    long nl = nextLong();
    if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
    throw new NumberFormatException();
    return (int) nl;
  }

  public double nextDouble() {
    return Double.parseDouble(next());
  }
}