# Right-Truncatable Prime

A Right-truncatable prime is a prime which remains prime when the last (“right”) digit is successively removed. For example, 239 is right-truncatable prime since 239, 23 and 2 are all prime. There are 83 right-truncatable primes.

The task is to check whether the given number (N > 0) is right-truncatable prime or not.

Examples:

```Input: 239
Output: Yes

Input: 101
Output: No
101 is not right-truncatable prime because
numbers formed are 101, 10 and 1. Here, 101
is prime but 10 and 1 are not prime.
```

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

The idea is to generate all the primes less than or equal to the given number N using Sieve of Eratosthenes. Once we have generated all such primes, then we check whether the number remains prime when the last (“right”) digit is successively removed.

## C++

 `// Program to check  ` `// whether a given number ` `// is right-truncatable  ` `// prime or not. ` `#include ` `using` `namespace` `std; ` ` `  `// Generate all prime numbers less than n. ` `bool` `sieveOfEratosthenes(``int` `n, ``bool` `isPrime[]) ` `{ ` `    ``// Initialize all entries ` `    ``// of boolean array as  ` `    ``// true. A value in ` `    ``// isPrime[i] will finally ` `    ``// be false if i is Not a  ` `    ``// prime, else true ` `    ``// bool isPrime[n+1]; ` `    ``isPrime = isPrime = ``false``; ` `    ``for``( ``int` `i = 2; i <= n; i++) ` `        ``isPrime[i] = ``true``; ` ` `  `    ``for` `(``int` `p = 2; p * p<=n; p++) ` `    ``{ ` ` `  `        ``// If isPrime[p] is not changed, then it is ` `        ``// a prime ` `        ``if` `(isPrime[p] == ``true``) ` `        ``{ ` `            ``// Update all multiples of p ` `            ``for` `(``int` `i = p * 2; i <= n; i += p) ` `                ``isPrime[i] = ``false``; ` ` `  `        ``} ` `    ``} ` `} ` ` `  `// Returns true if n is right-truncatable, ` `// else false ` `bool` `rightTruPrime(``int` `n) ` `{ ` `    ``// Generating primes using Sieve ` `    ``bool` `isPrime[n+1]; ` `    ``sieveOfEratosthenes(n, isPrime); ` ` `  `    ``// Checking whether the number remains ` `    ``// prime when the last ("right")  ` `    ``// digit is successively removed ` `    ``while` `(n) ` `    ``{ ` `        ``if` `(isPrime[n])  ` `            ``n = n / 10; ` `        ``else` `            ``return` `false``; ` `    ``} ` `    ``return` `true``;  ` `} ` ` `  `// Driver program ` `int` `main() ` `{ ` `    ``int` `n = 59399; ` `    ``if` `(rightTruPrime(n)) ` `        ``cout << ``"Yes"` `<< endl; ` `    ``else` `        ``cout << ``"No"` `<< endl; ` `    ``return` `0; ` `} `

## Java

 `// Java code to check  ` `// right-truncatable  ` `// prime or not. ` `import` `java.io.*; ` ` `  `class` `GFG { ` `     `  `    ``// Generate all prime ` `    ``// numbers less than n. ` `    ``static` `void` `sieveOfEratosthenes ` `                ``(``int` `n, ``boolean` `isPrime[])  ` `    ``{ ` `         `  `        ``// Initialize all entries of ` `        ``// boolean array as true. A ` `        ``// value in isPrime[i] will ` `        ``// finally be false if i is ` `        ``// Not a prime, else true ` `        ``// bool isPrime[n+1]; ` `        ``isPrime[``0``] = isPrime[``1``] = ``false``; ` `        ``for` `(``int` `i = ``2``; i <= n; i++) ` `            ``isPrime[i] = ``true``; ` `     `  `        ``for` `(``int` `p=``2``; p*p<=n; p++) ` `        ``{ ` `            ``// If isPrime[p] is not  ` `            ``// changed, then it  ` `            ``// is a prime ` `            ``if` `(isPrime[p] == ``true``) ` `            ``{ ` `                ``// Update all multiples of p ` `                ``for` `(``int` `i = p * ``2``; i <= n; i += p) ` `                    ``isPrime[i] = ``false``; ` `            ``} ` `        ``} ` `    ``} ` `     `  `    ``// Returns true if n is ` `    ``// right-truncatable,  ` `    ``// else false ` `    ``static` `boolean` `rightTruPrime(``int` `n) ` `     ``{ ` `         `  `        ``// Generating primes using Sieve ` `        ``boolean` `isPrime[] = ``new` `boolean``[n+``1``]; ` `        ``sieveOfEratosthenes(n, isPrime); ` `     `  `        ``// Checking whether the number ` `        ``// remains prime when the last (right) ` `        ``// digit is successively removed ` `        ``while` `(n != ``0``) ` `        ``{ ` `             `  `            ``if` `(isPrime[n]) ` `                ``n = n / ``10``;  ` `            ``else` `                ``return` `false``; ` `        ``} ` `        ``return` `true``; ` `    ``} ` `     `  `    ``// Driver program ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``int` `n = ``59399``; ` `         `  `        ``if` `(rightTruPrime(n)) ` `            ``System.out.println(``"Yes"``); ` `        ``else` `            ``System.out.println(``"No"``); ` `    ``} ` `} ` ` `  `/* This code is contributed by Nikita Tiwari.*/`

## Python3

 `# Python3 Program to check ` `# whether a given number ` `# is right-truncatable  ` `# prime or not. ` ` `  `# Generate all prime numbers less than n. ` `def` `sieveOfEratosthenes(n,isPrime) : ` `     `  `    ``# Initialize all entries  ` `    ``# of boolean array as  ` `    ``# true. A value in isPrime[i]  ` `    ``# will finally be false if ` `    ``# i is Not a prime, else true ` `    ``# bool isPrime[n+1]; ` `    ``isPrime[``0``] ``=` `isPrime[``1``] ``=` `False` `    ``for` `i ``in` `range``(``2``, n``+``1``) : ` `        ``isPrime[i] ``=` `True` `    ``p ``=` `2` `    ``while``(p ``*` `p <``=` `n) : ` `        ``# If isPrime[p] is not changed, then it is ` `        ``# a prime ` `        ``if` `(isPrime[p] ``=``=` `True``) : ` `            ``# Update all multiples of p ` `            ``i ``=` `p ``*` `2` `            ``while``(i <``=` `n) : ` `                ``isPrime[i] ``=` `False` `                ``i ``=` `i ``+` `p ` `        ``p ``=` `p ``+` `1` `         `  ` `  `# Returns true if n is right-truncatable, else false ` `def` `rightTruPrime(n) : ` `    ``# Generating primes using Sieve ` `    ``isPrime``=``[``None``] ``*` `(n``+``1``) ` `    ``sieveOfEratosthenes(n, isPrime) ` ` `  `    ``# Checking whether the  ` `    ``# number remains prime ` `    ``# when the last ("right") ` `    ``# digit is successively ` `    ``# removed ` `    ``while` `(n !``=` `0``) : ` `        ``if` `(isPrime[n]) : ` `            ``n ``=` `n ``/``/` `10`      `        ``else` `: ` `            ``return` `False`  `     `  `    ``return` `True` ` `  ` `  `# Driven program ` `n ``=` `59399` `if` `(rightTruPrime(n)) : ` `    ``print``(``"Yes"``) ` `else` `: ` `    ``print``(``"No"``) ` ` `  `# This code is contributed by Nikita Tiwari. `

## C#

 `// C# code to check right- ` `// truncatable prime or not ` `using` `System; ` ` `  `class` `GFG { ` ` `  `    ``// Generate all prime ` `    ``// numbers less than n. ` `    ``static` `void` `sieveOfEratosthenes(``int` `n, ``bool``[] isPrime) ` `    ``{ ` ` `  `        ``// Initialize all entries of ` `        ``// boolean array as true. A ` `        ``// value in isPrime[i] will ` `        ``// finally be false if i is ` `        ``// Not a prime, else true ` `        ``// bool isPrime[n+1]; ` `        ``isPrime = isPrime = ``false``; ` ` `  `        ``for` `(``int` `i = 2; i <= n; i++) ` `            ``isPrime[i] = ``true``; ` ` `  `        ``for` `(``int` `p = 2; p * p <= n; p++) { ` `            ``// If isPrime[p] is not ` `            ``// changed, then it ` `            ``// is a prime ` `            ``if` `(isPrime[p] == ``true``) { ` `                ``// Update all multiples of p ` `                ``for` `(``int` `i = p * 2; i <= n; i += p) ` `                    ``isPrime[i] = ``false``; ` `            ``} ` `        ``} ` `    ``} ` ` `  `    ``// Returns true if n is right- ` `    ``// truncatable,  else false ` `    ``static` `bool` `rightTruPrime(``int` `n) ` `    ``{ ` ` `  `        ``// Generating primes using Sieve ` `        ``bool``[] isPrime = ``new` `bool``[n + 1]; ` `        ``sieveOfEratosthenes(n, isPrime); ` ` `  `        ``// Checking whether the number ` `        ``// remains prime when last (right) ` `        ``// digit is successively removed ` `        ``while` `(n != 0) { ` ` `  `            ``if` `(isPrime[n]) ` `                ``n = n / 10; ` `            ``else` `                ``return` `false``; ` `        ``} ` `        ``return` `true``; ` `    ``} ` ` `  `    ``// Driven program ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int` `n = 59399; ` ` `  `        ``if` `(rightTruPrime(n)) ` `            ``Console.WriteLine(``"Yes"``); ` `        ``else` `            ``Console.WriteLine(``"No"``); ` `    ``} ` `} ` ` `  `// This code is contributed by Anant Agarwal `

## PHP

 ` `

Output:

```Yes
```

Related Article:Left-Truncatable Prime

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