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📜  索菲·格曼(Sophie Germain)Prime

📅  最后修改于: 2021-04-26 05:44:37             🧑  作者: Mango

编写程序以打印所有小于n的sophie germain数。如果2p + 1也是素数，则素数p称为sophie素数。数字2p + 1被称为安全素数。例如11是素数，而11 * 2 +1 = 23也是素数，因此11是sophie germain素数。前几个索菲德文素数是2、3、5、11、23、29、41、53、83、89、113、131、173、179 ..

例子： 

Input : 25
Output : 2 3 5 11 23

这是在n以下打印sophie germain编号的程序。
解决的方法很简单。为了获得n以下的所有sophie数，我们将进行循环直到n，对于循环中的每个数字，我们可以检查该数字和(2 * number + 1)两者是否都是质数，并且为了检查该数，我们使用了筛网方法。

以下是此方法的实现。

C++
// CPP program to print all sophie german
// prime number till n.
#include 
using namespace std;
  
// function to detect prime number
// here we have used sieve method
// https://www.geeksforgeeks.org/sieve-of-eratosthenes/
// to detect prime number
bool sieve(int n, bool prime[])
{
    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;
        }
    }
}
  
void printSophieGermanNumber(int n)
{
    // We have made array till 2*n +1
    // so that we can check prime number
    // till that and conclude about sophie
    // german prime .
    bool prime[2 * n + 1];
    memset(prime, true, sizeof(prime));
    sieve(2 * n + 1, prime);
  
    for (int i = 2; i <= n; ++i) {
  
        // checking every i whether it is
        // sophie german prime or not.
        if (prime[i] && prime[2 * i + 1]) 
            cout << i << " ";        
    }
}
  
int main()
{
    int n = 25;
    printSophieGermanNumber(n);
    return 0;
}

Java
// Java program to print all 
// sophie german prime number till n.
import java.io.*;
import java.util.*;
      
class GFG {
      
    // function to detect prime number
    // here we have used sieve method
    // https://www.geeksforgeeks.org/sieve-of-eratosthenes/
    // to detect prime number
    static void sieve(int n, boolean prime[])
    {
        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;
            }
        }
    }
      
    static void printSophieGermanNumber(int n)
    {
        // We have made array till 2*n +1
        // so that we can check prime number
        // till that and conclude about sophie
        // german prime .
        boolean prime[]=new boolean[2 * n + 1];
        Arrays.fill(prime,true);
        sieve(2 * n + 1, prime);
      
        for (int i = 2; i < n; ++i) {
      
            // checking every i whether it is
            // sophie german prime or not.
            if (prime[i] && prime[2 * i + 1]) 
                System.out.print( i + " ");     
        }
    }
      
    public static void main(String args[])
    {
        int n = 25;
        printSophieGermanNumber(n);
    }
}
  
// This code is contributed 
// by Nikita Tiwari.

Python3
# Python 3 program to print all sophie 
# german prime number till n.
  
# Function to detect prime number
# here we have used sieve method
# https://www.geeksforgeeks.org/sieve-of-eratosthenes/
# to detect prime number
def sieve(n, prime) :
    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, p) :
                prime[i] = False
                  
        p += 1
          
                  
def printSophieGermanNumber(n) :
    # We have made array till 2*n +1
    # so that we can check prime number
    # till that and conclude about sophie
    # german prime .
    prime = [True]*(2 * n + 1)
      
    sieve(2 * n + 1, prime)
  
    for i in range(2, n + 1) :
          
        # checking every i whether it is
        # sophie german prime or not.
        if (prime[i] and prime[2 * i + 1]) :
            print( i , end = " ")
              
  
# Driver Code
n = 25
printSophieGermanNumber(n)
  
  
# This code is contributed by Nikita Tiwari.

C#
// C# program to print 
// all sophie german 
// prime number till n.
using System;
      
class GFG
{
      
    // function to detect prime 
    // number here we have used 
    // sieve method 
    // https://www.geeksforgeeks.org/sieve-of-eratosthenes/
    // to detect prime number
    static void sieve(int n,
                      bool []prime)
    {
        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;
            }
        }
    }
      
    static void printSophieGermanNumber(int n)
    {
        // We have made array till 
        // 2*n +1 so that we can 
        // check prime number till 
        // that and conclude about 
        // sophie german prime .
        bool []prime = new bool[2 * n + 1];
        for (int i = 0; 
                 i < prime.Length; i++)
        {
            prime[i] = true;
        }
        sieve(2 * n + 1, prime);
      
        for (int i = 2; i < n; ++i) 
        {
      
            // checking every i whether 
            // it is sophie german prime
            // or not.
            if (prime[i] && prime[2 * i + 1]) 
                Console.Write( i + " ");     
        }
    }     
      
    // Driver code
    static void Main()
    {
        int n = 25;
        printSophieGermanNumber(n);
    }
} 
  
// This code is contributed by 
// Manish Shaw(manishshaw1)

PHP

输出 ： 

2 3 5 11 23

苏菲素数的应用：