Program för att hitta alla Mersenne Primes till N
Prova det på GfG Practice 
Mersenne Prime är ett primtal som är en mindre än en potens av två. Med andra ord är vilket primtal som helst Mersenne Prime om det har formen 2 k -1 där k är ett heltal större än eller lika med 2. De första Mersenne-primtalen är 3 7 31 och 127.
Uppgiften är att skriva ut alla Mersenne Primes mindre än ett inmatat positivt heltal n.
Exempel:
Input: 10
Output: 3 7
3 and 7 are prime numbers smaller than or
equal to 10 and are of the form 2 k -1
Input: 100
Output: 3 7 31
C++
Tanken är att generera alla primtal mindre än eller lika med det givna talet n med hjälp av Sil av Eratosthenes . När vi har genererat alla sådana primtal, itererar vi genom alla tal i formen 2 k -1 och kontrollera om de är primtal eller inte.
Nedan följer genomförandet av idén.
Java// Program to generate mersenne primes #includeusing namespace std ; // Generate all prime numbers less than n. void SieveOfEratosthenes ( int n bool prime []) { // Initialize all entries of boolean array // as true. A value in prime[i] will finally // be false if i is Not a prime else true // bool prime[n+1]; for ( int i = 0 ; i <= n ; i ++ ) prime [ i ] = true ; for ( int p = 2 ; p * p <= n ; p ++ ) { // If prime[p] is not changed then it // is a prime if ( prime [ p ] == true ) { // Update all multiples of p for ( int i = p * 2 ; i <= n ; i += p ) prime [ i ] = false ; } } } // Function to generate mersenne primes less // than or equal to n void mersennePrimes ( int n ) { // Create a boolean array 'prime[0..n]' bool prime [ n + 1 ]; // Generating primes using Sieve SieveOfEratosthenes ( n prime ); // Generate all numbers of the form 2^k - 1 // and smaller than or equal to n. for ( int k = 2 ; (( 1 < < k ) -1 ) <= n ; k ++ ) { long long num = ( 1 < < k ) - 1 ; // Checking whether number is prime and is // one less than the power of 2 if ( prime [ num ]) cout < < num < < ' ' ; } } // Driven program int main () { int n = 31 ; cout < < 'Mersenne prime numbers smaller ' < < 'than or equal to ' < < n < < endl ; mersennePrimes ( n ); return 0 ; } Python3// Program to generate // mersenne primes import java.io.* ; class GFG { // Generate all prime numbers // less than n. static void SieveOfEratosthenes ( int n boolean prime [] ) { // Initialize all entries of // boolean array as true. A // value in prime[i] will finally // be false if i is Not a prime // else true bool prime[n+1]; for ( int i = 0 ; i <= n ; i ++ ) prime [ i ] = true ; for ( int p = 2 ; p * p <= n ; p ++ ) { // If prime[p] is not changed // then it is a prime if ( prime [ p ] == true ) { // Update all multiples of p for ( int i = p * 2 ; i <= n ; i += p ) prime [ i ] = false ; } } } // Function to generate mersenne // primes lessthan or equal to n static void mersennePrimes ( int n ) { // Create a boolean array // 'prime[0..n]' boolean prime []= new boolean [ n + 1 ] ; // Generating primes // using Sieve SieveOfEratosthenes ( n prime ); // Generate all numbers of // the form 2^k - 1 and // smaller than or equal to n. for ( int k = 2 ; (( 1 < < k ) - 1 ) <= n ; k ++ ) { long num = ( 1 < < k ) - 1 ; // Checking whether number is // prime and is one less than // the power of 2 if ( prime [ ( int )( num ) ] ) System . out . print ( num + ' ' ); } } // Driven program public static void main ( String args [] ) { int n = 31 ; System . out . println ( 'Mersenne prime' + 'numbers smaller than' + 'or equal to ' + n ); mersennePrimes ( n ); } } // This code is contributed by Nikita Tiwari.C## Program to generate mersenne primes # Generate all prime numbers # less than n. def SieveOfEratosthenes ( n prime ): # Initialize all entries of boolean # array as true. A value in prime[i] # will finally be false if i is Not # a prime else true bool prime[n+1] for i in range ( 0 n + 1 ) : prime [ i ] = True p = 2 while ( p * p <= n ): # If prime[p] is not changed # then it is a prime if ( prime [ p ] == True ) : # Update all multiples of p for i in range ( p * 2 n + 1 p ): prime [ i ] = False p += 1 # Function to generate mersenne # primes less than or equal to n def mersennePrimes ( n ) : # Create a boolean array # 'prime[0..n]' prime = [ 0 ] * ( n + 1 ) # Generating primes using Sieve SieveOfEratosthenes ( n prime ) # Generate all numbers of the # form 2^k - 1 and smaller # than or equal to n. k = 2 while ((( 1 < < k ) - 1 ) <= n ): num = ( 1 < < k ) - 1 # Checking whether number # is prime and is one # less than the power of 2 if ( prime [ num ]) : print ( num end = ' ' ) k += 1 # Driver Code n = 31 print ( 'Mersenne prime numbers smaller' 'than or equal to ' n ) mersennePrimes ( n ) # This code is contributed # by SmithaJavaScript// C# Program to generate mersenne primes using System ; class GFG { // Generate all prime numbers less than n. static void SieveOfEratosthenes ( int n bool [] prime ) { // Initialize all entries of // boolean array as true. A // value in prime[i] will finally // be false if i is Not a prime // else true bool prime[n+1]; for ( int i = 0 ; i <= n ; i ++ ) prime [ i ] = true ; for ( int p = 2 ; p * p <= n ; p ++ ) { // If prime[p] is not changed // then it is a prime if ( prime [ p ] == true ) { // Update all multiples of p for ( int i = p * 2 ; i <= n ; i += p ) prime [ i ] = false ; } } } // Function to generate mersenne // primes lessthan or equal to n static void mersennePrimes ( int n ) { // Create a boolean array // 'prime[0..n]' bool [] prime = new bool [ n + 1 ]; // Generating primes // using Sieve SieveOfEratosthenes ( n prime ); // Generate all numbers of // the form 2^k - 1 and // smaller than or equal to n. for ( int k = 2 ; (( 1 < < k ) - 1 ) <= n ; k ++ ) { long num = ( 1 < < k ) - 1 ; // Checking whether number is // prime and is one less than // the power of 2 if ( prime [( int )( num )]) Console . Write ( num + ' ' ); } } // Driven program public static void Main () { int n = 31 ; Console . WriteLine ( 'Mersenne prime numbers' + ' smaller than or equal to ' + n ); mersennePrimes ( n ); } } // This code is contributed by nitin mittal.PHP< script > // JavaScript to generate // mersenne primes // Generate all prime numbers // less than n. function SieveOfEratosthenes ( n prime ) { // Initialize all entries of // boolean array as true. A // value in prime[i] will finally // be false if i is Not a prime // else true bool prime[n+1]; for ( let i = 0 ; i <= n ; i ++ ) prime [ i ] = true ; for ( let p = 2 ; p * p <= n ; p ++ ) { // If prime[p] is not changed // then it is a prime if ( prime [ p ] == true ) { // Update all multiples of p for ( let i = p * 2 ; i <= n ; i += p ) prime [ i ] = false ; } } } // Function to generate mersenne // primes lessthan or equal to n function mersennePrimes ( n ) { // Create a boolean array // 'prime[0..n]' let prime = []; // Generating primes // using Sieve SieveOfEratosthenes ( n prime ); // Generate all numbers of // the form 2^k - 1 and // smaller than or equal to n. for ( let k = 2 ; (( 1 < < k ) - 1 ) <= n ; k ++ ) { let num = ( 1 < < k ) - 1 ; // Checking whether number is // prime and is one less than // the power of 2 if ( prime [( num )]) document . write ( num + ' ' ); } } // Driver Code let n = 31 ; document . write ( 'Mersenne prime' + 'numbers smaller than' + 'or equal to ' + n + '
' ); mersennePrimes ( n ); // This code is contributed by code_hunt. < /script>Produktion:
Mersenne prime numbers smaller than or equal to 31
3 7 31Tidskomplexitet: O (n*log(logn))
Rymdkomplexitet: PÅ)
Skapa frågesport
Referenser:
https://en.wikipedia.org/wiki/Mersenne_prime
