# Right-Truncatable Prime

• Difficulty Level : Easy
• Last Updated : 25 Mar, 2021

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.```

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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[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``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[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` `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

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## Javascript

 ``

Output:

`Yes`

Related Article:Left-Truncatable Prime
References:
https://en.wikipedia.org/wiki/Truncatable_prime
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