Check if number can be made prime by deleting a single digit

Given an integer N, the task is to check if it is possible to make N prime by deleting any single digit from N.

Examples:

Input: N = 610
Output: Yes
Explanation: 
Deleting 0 from 610, we get 61 which is prime. 

Input: N = 68 
Output: No

Approach: The idea is to convert N to a string. Now iterate for every digit of string and Delete character at index i from string and then convert the string after deleting character at index i to an integer, Now check if this integer is a prime, then return true. Otherwise, finally return false.

Below is the implementation of the above approach:

C++

// C++ implementation to check if a number
// becomes prime by deleting any digit

#include <bits/stdc++.h>
using namespace std;

// Function to check if N is prime
bool isPrime(int n)
{
    // Corner cases
    if (n <= 1)
        return false;
    if (n <= 3)
        return true;

    // This is checked so that we can skip
    // middle five numbers in below loop
    if (n % 2 == 0 || n % 3 == 0)
        return false;

    for (int i = 5; i * i <= n; i = i + 6)
        if (n % i == 0 || n % (i + 2) == 0)
            return false;

    return true;
}

// Function to delete character at index i
// from given string str
string deleteIth(string str, int i)
{
    // Deletes character at position 4
    str.erase(str.begin() + i);

    return str;
}

// Function to check if a number
// becomes prime by deleting any digit
bool isPrimePossible(int N)
{
    // Converting the number to string
    string s = to_string(N);

    // length of string
    int l = s.length();

    // number should not be
    // of single digit
    if (l < 2)
        return false;

    // Loop to find all numbers
    // after deleting a single digit
    for (int i = 0; i < l ; i++) {

        // Deleting ith character
        // from the string
        string str = deleteIth(s, i);

        // converting string to int
        int num = stoi(str);

        if (isPrime(num))
            return true;
    }
    return false;
}

// Driver Code
int main()
{
    int N = 610;
    isPrimePossible(N) ? cout << "Yes"
                     : cout << "No";
    return 0;
}

Java

// Java implementation to check if a number
// becomes prime by deleting any digit
import java.util.*;
class GFG{

  // Function to check if N is prime
  static boolean isPrime(int n)
  {
    // Corner cases
    if (n <= 1)
      return false;
    if (n <= 3)
      return true;

    // This is checked so that we can skip
    // middle five numbers in below loop
    if (n % 2 == 0 || n % 3 == 0)
      return false;

    for (int i = 5; i * i <= n; i = i + 6)
      if (n % i == 0 || n % (i + 2) == 0)
        return false;

    return true;
  }

  // Function to delete character at index i
  // from given String str
  static String deleteIth(String str, int i)
  {
    // Deletes character at position 4
    str = str.substring(0, i) +
            str.substring(i + 1);

    return str;
  }

  // Function to check if a number
  // becomes prime by deleting any digit
  static boolean isPrimePossible(int N)
  {
    // Converting the number to String
    String s = String.valueOf(N);

    // length of String
    int l = s.length();

    // number should not be
    // of single digit
    if (l < 2)
      return false;

    // Loop to find all numbers
    // after deleting a single digit
    for (int i = 0; i < l; i++)
    {

      // Deleting ith character
      // from the String
      String str = deleteIth(s, i);

      // converting String to int
      int num = Integer.valueOf(str);

      if (isPrime(num))
        return true;
    }
    return false;
  }

  // Driver Code
  public static void main(String[] args)
  {
    int N = 610;
    if (isPrimePossible(N))
      System.out.print("Yes");
    else
      System.out.print("No");
  }
}

// This code is contributed by Rajput-Ji

Python3

# Python3 implementation to check if a number
# becomes prime by deleting any digit

# Function to check if N is prime
#from builtins import range
def isPrime(n):

    # Corner cases
    if (n <= 1):
        return False;
    if (n <= 3):
        return True;

    # This is checked so that we can skip
    # middle five numbers in below loop
    if (n % 2 == 0 or n % 3 == 0):
        return False;

    for i in range(5, int(n**1/2), 6):
        if (n % i == 0 or n % (i + 2) == 0):
            return False;

    return True;

# Function to delete character at index i
# from given String str
def deleteIth(str, i):

    # Deletes character at position 4
    str = str[0:i] + str[i + 1:];

    return str;

# Function to check if a number
# becomes prime by deleting any digit
def isPrimePossible(N):

    # Converting the number to String
    s = str(N);

    # length of String
    l = len(s);

    # number should not be
    # of single digit
    if (l < 2):
        return False;

    # Loop to find all numbers
    # after deleting a single digit
    for i in range(l):

        # Deleting ith character
        # from the String
        str1 = deleteIth(s, i);

        # converting String to int
        num = int(str1);

        if (isPrime(num)):
            return True;

    return False;

# Driver Code
if __name__ == '__main__':
    N = 610;
    if (isPrimePossible(N)):
        print("Yes");
    else:
        print("No");

# This code is contributed by Rajput-Ji

C#

// C# implementation to check if a number
// becomes prime by deleting any digit
using System;

class GFG{

// Function to check if N is prime
static bool isPrime(int n)
{

    // Corner cases
    if (n <= 1)
        return false;
    if (n <= 3)
        return true;

    // This is checked so that we can skip
    // middle five numbers in below loop
    if (n % 2 == 0 || n % 3 == 0)
        return false;

    for(int i = 5; i * i <= n; i = i + 6)
        if (n % i == 0 || n % (i + 2) == 0)
            return false;

    return true;
}

// Function to delete character at index i
// from given String str
static String deleteIth(String str, int i)
{

    // Deletes character at position 4
    str = str.Substring(0, i) +
          str.Substring(i + 1);

    return str;
}

// Function to check if a number
// becomes prime by deleting any digit
static bool isPrimePossible(int N)
{

    // Converting the number to String
    String s = String.Join("", N);

    // length of String
    int l = s.Length;

    // number should not be
    // of single digit
    if (l < 2)
        return false;

    // Loop to find all numbers
    // after deleting a single digit
    for(int i = 0; i < l; i++)
    {

        // Deleting ith character
        // from the String
        String str = deleteIth(s, i);

        // converting String to int
        int num = Int32.Parse(str);

        if (isPrime(num))
            return true;
    }
    return false;
}

// Driver Code
public static void Main(String[] args)
{
    int N = 610;

    if (isPrimePossible(N))
        Console.Write("Yes");
    else
        Console.Write("No");
}
}

// This code is contributed by Rajput-Ji

Javascript

<script>
// JavaScript implementation to check if a number
// becomes prime by deleting any digit

// Function to check if N is prime
  function isPrime(n)
  {
    // Corner cases
    if (n <= 1)
      return false;
    if (n <= 3)
      return true;

    // This is checked so that we can skip
    // middle five numbers in below loop
    if (n % 2 == 0 || n % 3 == 0)
      return false;

    for (let i = 5; i * i <= n; i = i + 6)
      if (n % i == 0 || n % (i + 2) == 0)
        return false;

    return true;
  }

  // Function to delete character at index i
  // from given String str
  function deleteIth(str, i)
  {
    // Deletes character at position 4
    str = str.substr(0, i) +
            str.substr(i + 1);

    return str;
  }

  // Function to check if a number
  // becomes prime by deleting any digit
 function isPrimePossible(N)
  {
    // Converting the number to String
    let s = N.toString();

    // length of String
    let l = s.length;

    // number should not be
    // of single digit
    if (l < 2)
      return false;

    // Loop to find all numbers
    // after deleting a single digit
    for (let i = 0; i < l; i++)
    {

      // Deleting ith character
      // from the String
      let str = deleteIth(s, i);

      // converting String to let
      let num = parseInt(str);

      if (isPrime(num))
        return true;
    }
    return false;
  }

// Driver Code

    let N = 610;
    if (isPrimePossible(N))
      document.write("Yes");
    else
      document.write("No");

</script>

Output

Yes

Time Complexity: O(D)
Auxiliary Space: O(1)