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.
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++
//C++ Program to check // whether a given number// is right-truncatable // prime or not.#include<bits/stdc++.h>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 falsebool 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 programint 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 falsedef 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 programn = 59399if (rightTruPrime(n)) : print("Yes")else : print("No")# This code is contributed by Nikita Tiwari. |
C#
// C# code to check right-// truncatable prime or notusing 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
<?php// Program to check whether a given number // is right-truncatable prime or not. // Generate all prime numbers less than n. function 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] = $isPrime[1] = false; for ($p = 2; $p * $p <= $n; $p++) { // If isPrime[p] is not changed, // then it is a prime if ($isPrime[$p] == true) { // Update all multiples of p for ($i = $p * 2; $i <= $n; $i += $p) $isPrime[$i] = false; } } } // Returns true if n is right-truncatable, // else false function rightTruPrime($n) { // Generating primes using Sieve $isPrime = array_fill(0, $n + 1, true); sieveOfEratosthenes($n, $isPrime); // Checking whether the number remains // prime when the last ("right") // digit is successively removed while ($n) { if ($isPrime[$n]) $n = (int)($n / 10); else return false; } return true; } // Driver Code$n = 59399; if (rightTruPrime($n)) echo "Yes\n"; else echo "No\n"; // This code is contributed by mits?> |
Javascript
<script>// javascript code to check // right-truncatable // prime or not. // Generate all prime // numbers less than n. function 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 (let i = 2; i <= n; i++) isPrime[i] = true; for (let 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 (let i = p * 2; i <= n; i += p) isPrime[i] = false; } } } // Returns true if n is // right-truncatable, // else false function rightTruPrime(n) { // Generating primes using Sieve let isPrime = new Array(n + 1).fill(false); sieveOfEratosthenes(n, isPrime); // Checking whether the number // remains prime when the last (right) // digit is successively removed while (n != 0) { if (isPrime[n]) n = parseInt(n / 10); else return false; } return true; } // Driver program var n = 59399; if (rightTruPrime(n)) document.write("Yes"); else document.write("No");// This code is contributed by shikhasingrajput</script> |
Output:
Yes
Related Article:Left-Truncatable Prime
References:
https://en.wikipedia.org/wiki/Truncatable_prime
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