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Primo troncabile a destra

Un primo troncabile a destra è un primo che rimane primo quando l'ultima cifra ("destra") viene successivamente rimossa. Ad esempio 239 è un primo troncabile a destra poiché 239 23 e 2 sono tutti primi. Ci sono 83 numeri primi troncabili a destra.
Il compito è verificare se il numero dato (N > 0) è primo troncabile a destra oppure no. 
Esempi:  
 

cambiare il nome della directory linux
  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.


 


L'idea è di generare tutti i numeri primi inferiori o uguali al numero N specificato utilizzando Setaccio di Eratostene . Una volta che abbiamo generato tutti questi numeri primi, controlliamo se il numero rimane primo quando l'ultima cifra ("destra") viene successivamente rimossa.
 



C++
//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(nisPrime) : # 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
 // 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 'Yesn'; else echo 'Non'; // 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> 

Produzione:  
 

Yes


Articolo correlato: Primo troncabile a sinistra
Riferimenti:  
https://en.wikipedia.org/wiki/Truncatable_prime
 

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