# Find the sum of all Truncatable primes below N

Given an integer N, the task is to find the sum of all Truncatable primes below N. Truncatable prime is a number which is left-truncatable prime (if the leading (“left”) digit is successively removed, then all resulting numbers are prime) as well as right-truncatable prime (if the last (“right”) digit is successively removed, then all the resulting numbers are prime).
For example, 3797 is left-truncatable prime because 797, 97 and 7 are primes. And, 3797 is also right-truncatable prime as 379, 37, and 3 are primes. Hence 3797 is a truncatable prime.

Examples:

Input: N = 25
Output: 40
2, 3, 5, 7 and 23 are the only truncatable primes below 25.
2 + 3 + 5 + 7 + 23 = 40

Input: N = 40
Output: 77

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: An efficient approach is to find all the prime numbers using Sieve of Eratosthenes and for every number below N check whether it is Truncatable prime or not. If yes then add is to the running sum.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` `#define N 1000005 ` ` `  `// To check if a number is prime or not ` `bool` `prime[N]; ` ` `  `// Sieve of Eratosthenes ` `// function to find all prime numbers ` `void` `sieve() ` `{ ` `    ``memset``(prime, ``true``, ``sizeof` `prime); ` `    ``prime = ``false``; ` `    ``prime = ``false``; ` ` `  `    ``for` `(``int` `i = 2; i < N; i++) ` `        ``if` `(prime[i]) ` `            ``for` `(``int` `j = i * 2; j < N; j += i) ` `                ``prime[j] = ``false``; ` `} ` ` `  `// Function to return the sum of ` `// all truncatable primes below n ` `int` `sumTruncatablePrimes(``int` `n) ` `{ ` `    ``// To store the required sum ` `    ``int` `sum = 0; ` ` `  `    ``// Check every number below n ` `    ``for` `(``int` `i = 2; i < n; i++) { ` ` `  `        ``int` `num = i; ` `        ``bool` `flag = ``true``; ` ` `  `        ``// Check from right to left ` `        ``while` `(num) { ` ` `  `            ``// If number is not prime at any stage ` `            ``if` `(!prime[num]) { ` `                ``flag = ``false``; ` `                ``break``; ` `            ``} ` `            ``num /= 10; ` `        ``} ` ` `  `        ``num = i; ` `        ``int` `power = 10; ` ` `  `        ``// Check from left to right ` `        ``while` `(num / power) { ` ` `  `            ``// If number is not prime at any stage ` `            ``if` `(!prime[num % power]) { ` `                ``flag = ``false``; ` `                ``break``; ` `            ``} ` `            ``power *= 10; ` `        ``} ` ` `  `        ``// If flag is still true ` `        ``if` `(flag) ` `            ``sum += i; ` `    ``} ` ` `  `    ``// Return the required sum ` `    ``return` `sum; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `n = 25; ` `    ``sieve(); ` `    ``cout << sumTruncatablePrimes(n); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach ` `import` `java.util.*; ` ` `  `class` `GFG  ` `{ ` ` `  `    ``static` `final` `int` `N = ``1000005``; ` ` `  `    ``// To check if a number is prime or not ` `    ``static` `boolean` `prime[] = ``new` `boolean``[N]; ` ` `  `    ``// Sieve of Eratosthenes ` `    ``// function to find all prime numbers ` `    ``static` `void` `sieve()  ` `    ``{ ` `        ``Arrays.fill(prime, ``true``); ` `        ``prime[``1``] = ``false``; ` `        ``prime[``0``] = ``false``; ` ` `  `        ``for` `(``int` `i = ``2``; i < N; i++)  ` `        ``{ ` `            ``if` `(prime[i])  ` `            ``{ ` `                ``for` `(``int` `j = i * ``2``; j < N; j += i) ` `                ``{ ` `                    ``prime[j] = ``false``; ` `                ``} ` `            ``} ` `        ``} ` `    ``} ` ` `  `    ``// Function to return the sum of ` `    ``// all truncatable primes below n ` `    ``static` `int` `sumTruncatablePrimes(``int` `n)  ` `    ``{ ` `        ``// To store the required sum ` `        ``int` `sum = ``0``; ` ` `  `        ``// Check every number below n ` `        ``for` `(``int` `i = ``2``; i < n; i++)  ` `        ``{ ` ` `  `            ``int` `num = i; ` `            ``boolean` `flag = ``true``; ` ` `  `            ``// Check from right to left ` `            ``while` `(num > ``0``) ` `            ``{ ` ` `  `                ``// If number is not prime at any stage ` `                ``if` `(!prime[num])  ` `                ``{ ` `                    ``flag = ``false``; ` `                    ``break``; ` `                ``} ` `                ``num /= ``10``; ` `            ``} ` ` `  `            ``num = i; ` `            ``int` `power = ``10``; ` ` `  `            ``// Check from left to right ` `            ``while` `(num / power > ``0``) ` `            ``{ ` ` `  `                ``// If number is not prime at any stage ` `                ``if` `(!prime[num % power]) ` `                ``{ ` `                    ``flag = ``false``; ` `                    ``break``; ` `                ``} ` `                ``power *= ``10``; ` `            ``} ` ` `  `            ``// If flag is still true ` `            ``if` `(flag)  ` `            ``{ ` `                ``sum += i; ` `            ``} ` `        ``} ` ` `  `        ``// Return the required sum ` `        ``return` `sum; ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `main(String[] args)  ` `    ``{ ` `        ``int` `n = ``25``; ` `        ``sieve(); ` `        ``System.out.println(sumTruncatablePrimes(n)); ` `    ``} ` `} ` ` `  `// This code contributed by Rajput-Ji `

## Python3

 `# Python3 implementation of the  ` `# above approach  ` `N ``=` `1000005` ` `  `# To check if a number is prime or not ` `prime ``=` `[``True` `for` `i ``in` `range``(N)] ` ` `  `# Sieve of Eratosthenes ` `# function to find all prime numbers ` `def` `sieve(): ` `    ``prime[``1``] ``=` `False` `    ``prime[``0``] ``=` `False` ` `  `    ``for` `i ``in` `range``(``2``, N): ` `        ``if` `(prime[i]``=``=``True``): ` `            ``for` `j ``in` `range``(i ``*` `2``, N, i): ` `                ``prime[j] ``=` `False` ` `  `# Function to return the sum of ` `# all truncatable primes below n ` `def` `sumTruncatablePrimes(n): ` ` `  `    ``# To store the required sum ` `    ``sum` `=` `0` ` `  `    ``# Check every number below n ` `    ``for` `i ``in` `range``(``2``, n): ` ` `  `        ``num ``=` `i ` `        ``flag ``=` `True` ` `  `        ``# Check from right to left ` `        ``while` `(num): ` ` `  `            ``# If number is not prime at any stage ` `            ``if` `(prime[num] ``=``=` `False``): ` `                ``flag ``=` `False` `                ``break` ` `  `            ``num ``/``/``=` `10` ` `  `        ``num ``=` `i ` `        ``power ``=` `10` ` `  `        ``# Check from left to right ` `        ``while` `(num ``/``/` `power): ` ` `  `            ``# If number is not prime at any stage ` `            ``if` `(prime[num ``%` `power] ``=``=` `False``): ` `                ``flag ``=` `False` `                ``break` ` `  `            ``power ``*``=` `10` ` `  `        ``# If flag is still true ` `        ``if` `(flag``=``=``True``): ` `            ``sum` `+``=` `i ` ` `  `    ``# Return the required sum ` `    ``return` `sum` ` `  `# Driver code ` `n ``=` `25` `sieve() ` `print``(sumTruncatablePrimes(n)) ` ` `  `# This code is contributed by mohit kumar `

## C#

 `// C# implementation of the above approach.  ` `using` `System; ` `using` `System.Collections.Generic; ` ` `  `class` `GFG  ` `{  ` ` `  `    ``static` `int` `N = 1000005;  ` ` `  `    ``// To check if a number is prime or not  ` `    ``static` `Boolean []prime = ``new` `Boolean[N];  ` ` `  `    ``// Sieve of Eratosthenes  ` `    ``// function to find all prime numbers  ` `    ``static` `void` `sieve()  ` `    ``{  ` `        ``Array.Fill(prime, ``true``);  ` `        ``prime = ``false``;  ` `        ``prime = ``false``;  ` ` `  `        ``for` `(``int` `i = 2; i < N; i++)  ` `        ``{  ` `            ``if` `(prime[i])  ` `            ``{  ` `                ``for` `(``int` `j = i * 2; j < N; j += i)  ` `                ``{  ` `                    ``prime[j] = ``false``;  ` `                ``}  ` `            ``}  ` `        ``}  ` `    ``}  ` ` `  `    ``// Function to return the sum of  ` `    ``// all truncatable primes below n  ` `    ``static` `int` `sumTruncatablePrimes(``int` `n)  ` `    ``{  ` `        ``// To store the required sum  ` `        ``int` `sum = 0;  ` ` `  `        ``// Check every number below n  ` `        ``for` `(``int` `i = 2; i < n; i++)  ` `        ``{  ` ` `  `            ``int` `num = i;  ` `            ``Boolean flag = ``true``;  ` ` `  `            ``// Check from right to left  ` `            ``while` `(num > 0)  ` `            ``{  ` ` `  `                ``// If number is not prime at any stage  ` `                ``if` `(!prime[num])  ` `                ``{  ` `                    ``flag = ``false``;  ` `                    ``break``;  ` `                ``}  ` `                ``num /= 10;  ` `            ``}  ` ` `  `            ``num = i;  ` `            ``int` `power = 10;  ` ` `  `            ``// Check from left to right  ` `            ``while` `(num / power > 0)  ` `            ``{  ` ` `  `                ``// If number is not prime at any stage  ` `                ``if` `(!prime[num % power])  ` `                ``{  ` `                    ``flag = ``false``;  ` `                    ``break``;  ` `                ``}  ` `                ``power *= 10;  ` `            ``}  ` ` `  `            ``// If flag is still true  ` `            ``if` `(flag)  ` `            ``{  ` `                ``sum += i;  ` `            ``}  ` `        ``}  ` ` `  `        ``// Return the required sum  ` `        ``return` `sum;  ` `    ``}  ` ` `  `    ``// Driver code  ` `    ``public` `static` `void` `Main(String []args)  ` `    ``{  ` `        ``int` `n = 25;  ` `        ``sieve();  ` `        ``Console.WriteLine(sumTruncatablePrimes(n));  ` `    ``}  ` ` `  `}  ` ` `  `// This code has been contributed by Arnab Kundu `

## PHP

 ` `

Output:

```40
```

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