# Find a prime number S containing given number N in it

Given an integer **N**, find a prime number **S** such that all digits of **N** occur in a contiguous sequence. There may be multiple answers. Print any one of them.

**Example:**

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Input:N = 42Output:42013Explanation:42013 is a prime and 42 occurs as a contiguous number in it. 15427 is also a correct answer.

Input:N = 47Output:47Explanation:47 itself is a prime

**Naive Approach: **Below steps can be followed:

- Iterate through all the numbers starting from
**N** - Convert every number into a string with to_string() function
- Check for the required substring using str.find() function
- If there is any number that has
**N**as a substring and it is prime then return that number

**Time Complexity: **O(S), where S is the required prime number

**Efficient Approach: **Below steps can be followed:

- The fact can be used that
**a number with value upto 1e12, between two consecutive primes, there are at most 464 non-prime numbers.** - Extend the current number
**N**by multiplying by 1000. - After that iterate through the next numbers one by one and check each of them.
- If the number is prime then print that number.
- It is easy to see that the first condition will always follow as the digits except the last three will be N.

Below is the implementation of the above approach:

## C++

`// C++ Implementation for the above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to check if a number is prime` `bool` `isPrime(` `long` `long` `N)` `{` ` ` `if` `(N == 1)` ` ` `return` `false` `;` ` ` `for` `(` `long` `long` `i = 2; i <= ` `sqrt` `(N); i++)` ` ` `// If N is divisible then its not a prime` ` ` `if` `(N % i == 0)` ` ` `return` `false` `;` ` ` `return` `true` `;` `}` `// Function to print a prime number` `// which has N as a substring` `long` `long` `prime_substring_Number(` `long` `long` `N)` `{` ` ` `// Check for the base case` ` ` `if` `(N == 0) {` ` ` `return` `103;` ` ` `// 103 is a prime` ` ` `}` ` ` `// multiply N by 10^3` ` ` `// Check for numbers from` ` ` `// N*1000 to N*1000 + 464` ` ` `N *= 1000;` ` ` `for` `(` `long` `long` `i = N; i < N + 465; i++) {` ` ` `if` `(isPrime(i)) {` ` ` `return` `i;` ` ` `}` ` ` `}` ` ` `return` `0;` `}` `// Driver Code` `int` `main()` `{` ` ` `long` `N = 42;` ` ` `cout << prime_substring_Number(N);` `}` |

## Java

`/*package whatever //do not write package name here */` `import` `java.io.*;` `class` `GFG {` `static` `boolean` `isPrime(` `long` `N)` `{` ` ` `if` `(N == ` `1` `)` ` ` `return` `false` `;` ` ` `for` `(` `long` `i = ` `2` `; i <= Math.sqrt(N); i++)` ` ` `// If N is divisible then its not a prime` ` ` `if` `(N % i == ` `0` `)` ` ` `return` `false` `;` ` ` `return` `true` `;` `}` ` ` `// Function to print a prime number` `// which has N as a substring` `static` `long` `prime_substring_Number(` `long` `N)` `{` ` ` `// Check for the base case` ` ` `if` `(N == ` `0` `) {` ` ` `return` `103` `;` ` ` `// 103 is a prime` ` ` `}` ` ` `// multiply N by 10^3` ` ` `// Check for numbers from` ` ` `// N*1000 to N*1000 + 464` ` ` `N *= ` `1000` `;` ` ` `for` `(` `long` `i = N; i < N + ` `465` `; i++) {` ` ` `if` `(isPrime(i)) {` ` ` `return` `i;` ` ` `}` ` ` `}` ` ` `return` `0` `;` `}` `// Driver Code` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `long` `N = ` `42` `;` ` ` `System.out.println(prime_substring_Number(N));` ` ` `}` `}` `// This code is contributed by maddler.` |

## Python3

`# python Implementation for the above approach` `# importing math library` `from` `math ` `import` `*` `# Function to check if a number is prime` `def` `isPrime(N) :` ` ` `if` `N > ` `1` `:` ` ` ` ` `# Iterate from 2 to n / 2` ` ` `for` `i ` `in` `range` `(` `2` `, ` `int` `(N` `/` `2` `)` `+` `1` `):` ` ` ` ` `# If num is divisible by any number between` ` ` `# 2 and n / 2, it is not prime` ` ` `if` `(N ` `%` `i) ` `=` `=` `0` `:` ` ` `return` `False` ` ` `else` `:` ` ` `return` `True` ` ` `else` `:` ` ` `return` `False` ` ` `# Function to print a prime number` `# which has N as a substring` `def` `prime_substring_Number(N) :` ` ` ` ` `# Check for the base case` ` ` `if` `(N ` `=` `=` `0` `) :` ` ` `return` `103` ` ` `# 103 is a prime` ` ` `# multiply N by 10^3` ` ` `# Check for numbers from` ` ` `# N*1000 to N*1000 + 464` ` ` `N ` `=` `N ` `*` `1000` ` ` `for` `i ` `in` `range` `(N,N ` `+` `465` `):` ` ` `if` `(isPrime(i)) :` ` ` `return` `i` ` ` ` ` `return` `0` `# Driver Code` `N ` `=` `42` `print` `(prime_substring_Number(N))` `# This code is contributed by anudeep23042002.` |

## C#

`// C# Implementation for the above approach` `using` `System;` `class` `GFG {` ` ` `// Function to check if a number is prime` ` ` `static` `bool` `isPrime(` `long` `N)` ` ` `{` ` ` `if` `(N == 1)` ` ` `return` `false` `;` ` ` `for` `(` `long` `i = 2; i <= Math.Sqrt(N); i++)` ` ` `// If N is divisible then its not a prime` ` ` `if` `(N % i == 0)` ` ` `return` `false` `;` ` ` `return` `true` `;` ` ` `}` ` ` `// Function to print a prime number` ` ` `// which has N as a substring` ` ` `static` `long` `prime_substring_Number(` `long` `N)` ` ` `{` ` ` `// Check for the base case` ` ` `if` `(N == 0) {` ` ` `return` `103;` ` ` `// 103 is a prime` ` ` `}` ` ` `// multiply N by 10^3` ` ` `// Check for numbers from` ` ` `// N*1000 to N*1000 + 464` ` ` `N *= 1000;` ` ` `for` `(` `long` `i = N; i < N + 465; i++) {` ` ` `if` `(isPrime(i)) {` ` ` `return` `i;` ` ` `}` ` ` `}` ` ` `return` `0;` ` ` `}` ` ` `// Driver Code` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `long` `N = 42;` ` ` `Console.WriteLine(prime_substring_Number(N));` ` ` `}` `}` `// This code is contributed y ukasp.` |

## Javascript

`<script>` ` ` `// JavaScript Program to implement` ` ` `// the above approach` ` ` `// Function to check if a number is prime` ` ` `function` `isPrime(N) {` ` ` `if` `(N == 1)` ` ` `return` `false` `;` ` ` `for` `(let i = 2; i <= Math.sqrt(N); i++)` ` ` `// If N is divisible then its not a prime` ` ` `if` `(N % i == 0)` ` ` `return` `false` `;` ` ` `return` `true` `;` ` ` `}` ` ` ` ` `// Function to print a prime number` ` ` `// which has N as a substring` ` ` `function` `prime_substring_Number(N)` ` ` `{` ` ` ` ` `// Check for the base case` ` ` `if` `(N == 0) {` ` ` `return` `103;` ` ` `// 103 is a prime` ` ` `}` ` ` `// multiply N by 10^3` ` ` `// Check for numbers from` ` ` `// N*1000 to N*1000 + 464` ` ` `N *= 1000;` ` ` `for` `(let i = N; i < N + 465; i++) {` ` ` `if` `(isPrime(i)) {` ` ` `return` `i;` ` ` `}` ` ` `}` ` ` `return` `0;` ` ` `}` ` ` `// Driver Code` ` ` `let N = 42;` ` ` `document.write(prime_substring_Number(N));` `// This code is contributed by Potta Lokesh` ` ` `</script>` |

**Output**

42013

**Time Complexity: **O(sqrt(N*1000)*300)**Auxiliary Space: **O(1)