العدد الأولي القابل للاقتطاع من اليمين هو عدد أولي يظل أوليًا عند إزالة الرقم الأخير ("الأيمن") على التوالي. على سبيل المثال، 239 هو عدد أولي قابل للاقتطاع من اليمين، حيث أن 239 23 و2 كلها أعداد أولية. هناك 83 عددًا أوليًا قابلاً للاقتطاع.
وتتمثل المهمة في التحقق مما إذا كان الرقم المحدد (N > 0) أوليًا قابلاً للاقتطاع من اليمين أم لا.
أمثلة:
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.
np.random.rand
الفكرة هي توليد جميع الأعداد الأولية الأصغر من أو تساوي الرقم المعطى N باستخدام غربال إراتوستينس . بمجرد إنشاء كل هذه الأعداد الأولية، فإننا نتحقق مما إذا كان الرقم يظل أوليًا عند إزالة الرقم الأخير ('الأيمن') على التوالي.
في أي عام تم اختراع الكمبيوترC++
//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>
الإخراج:
Yes
مقالة ذات صلة: رئيس الوزراء الأيسر القابل للاقتطاع
مراجع:
https://en.wikipedia.org/wiki/Truncatable_prime