Print all safe primes below N

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Given an integer N, the task is to print all safe primes below N safe primes. A safe prime is a prime number of the form (2 * p) + 1 where p is also a prime.

The first few safe primes are 5, 7, 11, 23, 47, …

Examples:

Input: N = 13
Output: 5 7 11
5 = 2 * 2 + 1
7 = 2 * 3 + 1
11 = 2 * 5 + 1

Input: N = 6
Output: 5 7

Approach: First pre-compute all the primes till N using Sieve of Eratosthenes and then starting from 2 check whether the current prime is also a safe prime. If yes then print it else skip to the next prime.

Below is the implementation of above approach:

C++

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to print first n safe primes
void printSafePrimes(int n)
{
    int prime[n + 1];
 
    // Initialize all entries of integer array
    // as 1. A value in prime[i] will finally
    // be 0 if i is Not a prime, else 1
    for (int i = 2; i <= n; i++)
        prime[i] = 1;
 
    // 0 and 1 are not primes
    prime[0] = prime[1] = 0;
 
    for (int p = 2; p * p <= n; p++) {
 
        // If prime[p] is not changed, then
        //  it is a prime
        if (prime[p] == 1) {
 
            // Update all multiples of p
            for (int i = p * 2; i <= n; i += p)
                prime[i] = 0;
        }
    }
 
    for (int i = 2; i <= n; i++) {
 
        // If i is prime
        if (prime[i] != 0) {
 
            // 2p + 1
            int temp = (2 * i) + 1;
 
            // If 2p + 1 is also a prime
            // then set prime[2p + 1] = 2
            if (temp <= n && prime[temp] != 0)
                prime[temp] = 2;
        }
    }
 
    for (int i = 5; i <= n; i++)
 
        // i is a safe prime
        if (prime[i] == 2)
            cout << i << " ";
}
 
// Driver code
int main()
{
    int n = 20;
    printSafePrimes(n);
    return 0;
}

Java

// Java implementation of the approach 
class GFG{
     
    // Function to print first n safe primes 
    static void printSafePrimes(int n) 
    { 
        int prime[] = new int [n + 1]; 
     
        // Initialize all entries of integer array 
        // as 1. A value in prime[i] will finally 
        // be 0 if i is Not a prime, else 1 
        for (int i = 2; i <= n; i++) 
            prime[i] = 1; 
     
        // 0 and 1 are not primes 
        prime[0] = prime[1] = 0; 
     
        for (int p = 2; p * p <= n; p++)
        { 
     
            // If prime[p] is not changed, then 
            // it is a prime 
            if (prime[p] == 1)
            { 
     
                // Update all multiples of p 
                for (int i = p * 2; i <= n; i += p) 
                    prime[i] = 0; 
            } 
        } 
     
        for (int i = 2; i <= n; i++)
        { 
     
            // If i is prime 
            if (prime[i] != 0)
            { 
     
                // 2p + 1 
                int temp = (2 * i) + 1; 
     
                // If 2p + 1 is also a prime 
                // then set prime[2p + 1] = 2 
                if (temp <= n && prime[temp] != 0) 
                    prime[temp] = 2; 
            } 
        } 
     
        for (int i = 5; i <= n; i++) 
     
            // i is a safe prime 
            if (prime[i] == 2) 
                System.out.print(i + " "); 
    } 
     
    // Driver code 
    public static void main(String []args)
    { 
        int n = 20; 
        printSafePrimes(n); 
    } 
}
 
// This code is contributed by Ryuga

Python3

# Python 3 implementation of the approach
from math import sqrt
 
# Function to print first n safe primes
def printSafePrimes(n):
    prime = [0 for i in range(n + 1)]
 
    # Initialize all entries of integer 
    # array as 1. A value in prime[i] 
    # will finally be 0 if i is Not a
    # prime, else 1
    for i in range(2, n + 1):
        prime[i] = 1
 
    # 0 and 1 are not primes
    prime[0] = prime[1] = 0
 
    for p in range(2, int(sqrt(n)) + 1, 1):
         
        # If prime[p] is not changed, 
        # then it is a prime
        if (prime[p] == 1):
             
            # Update all multiples of p
            for i in range(p * 2, n + 1, p):
                prime[i] = 0
     
    for i in range(2, n + 1, 1):
         
        # If i is prime
        if (prime[i] != 0):
             
            # 2p + 1
            temp = (2 * i) + 1
 
            # If 2p + 1 is also a prime
            # then set prime[2p + 1] = 2
            if (temp <= n and prime[temp] != 0):
                prime[temp] = 2
 
    for i in range(5, n + 1):
         
        # i is a safe prime
        if (prime[i] == 2):
            print(i, end = " ")
 
# Driver code
if __name__ == '__main__':
    n = 20
    printSafePrimes(n)
     
# This code is contributed by
# Sanjit_Prasad

C#

// C# implementation of the approach 
using System;
 
class GFG{
     
    // Function to print first n safe primes 
    static void printSafePrimes(int n) 
    { 
        int[] prime = new int [n + 1]; 
     
        // Initialize all entries of integer array 
        // as 1. A value in prime[i] will finally 
        // be 0 if i is Not a prime, else 1 
        for (int i = 2; i <= n; i++) 
            prime[i] = 1; 
     
        // 0 and 1 are not primes 
        prime[0] = prime[1] = 0; 
     
        for (int p = 2; p * p <= n; p++)
        { 
     
            // If prime[p] is not changed, then 
            // it is a prime 
            if (prime[p] == 1)
            { 
     
                // Update all multiples of p 
                for (int i = p * 2; i <= n; i += p) 
                    prime[i] = 0; 
            } 
        } 
     
        for (int i = 2; i <= n; i++)
        { 
     
            // If i is prime 
            if (prime[i] != 0)
            { 
     
                // 2p + 1 
                int temp = (2 * i) + 1; 
     
                // If 2p + 1 is also a prime 
                // then set prime[2p + 1] = 2 
                if (temp <= n && prime[temp] != 0) 
                    prime[temp] = 2; 
            } 
        } 
     
        for (int i = 5; i <= n; i++) 
     
            // i is a safe prime 
            if (prime[i] == 2) 
                Console.Write(i + " "); 
    } 
     
    // Driver code 
    public static void Main()
    { 
        int n = 20; 
        printSafePrimes(n); 
    } 
}
 
// This code is contributed by Ita_c.

PHP

<?php
// PHP implementation of the approach 
 
// Function to print first n safe primes 
function printSafePrimes($n) 
{ 
    $prime = array();
 
    // Initialize all entries of integer array 
    // as 1. A value in prime[i] will finally 
    // be 0 if i is Not a prime, else 1 
    for ($i = 2; $i <= $n; $i++) 
        $prime[$i] = 1; 
 
    // 0 and 1 are not primes 
    $prime[0] = $prime[1] = 0; 
 
    for ($p = 2; $p * $p <= $n; $p++) 
    { 
 
        // If prime[p] is not changed, 
        // then it is a prime 
        if ($prime[$p] == 1)
        { 
 
            // Update all multiples of p 
            for ($i = $p * 2; 
                 $i <= $n; $i += $p) 
                $prime[$i] = 0; 
        } 
    } 
 
    for ($i = 2; $i <= $n; $i++) 
    { 
 
        // If i is prime 
        if ($prime[$i] != 0) 
        { 
 
            // 2p + 1 
            $temp = (2 * $i) + 1; 
 
            // If 2p + 1 is also a prime 
            // then set prime[2p + 1] = 2 
            if ($temp <= $n && 
                $prime[$temp] != 0) 
                $prime[$temp] = 2; 
        } 
    } 
 
    for ($i = 5; $i <= $n; $i++) 
 
        // i is a safe prime 
        if ($prime[$i] == 2) 
            echo $i, " "; 
} 
 
// Driver code 
$n = 20; 
printSafePrimes($n); 
 
// This code is contributed 
// by aishwarya.27
?>

Javascript

<script>
 
// Javascript implementation of the approach 
 
// Function to print first n safe primes 
function printSafePrimes(n)
{
    let prime = new Array(n + 1); 
   
    // Initialize all entries of integer array 
    // as 1. A value in prime[i] will finally 
    // be 0 if i is Not a prime, else 1 
    for(let i = 2; i <= n; i++) 
        prime[i] = 1; 
   
    // 0 and 1 are not primes 
    prime[0] = prime[1] = 0; 
   
    for(let p = 2; p * p <= n; p++)
    { 
         
        // If prime[p] is not changed, then 
        // it is a prime 
        if (prime[p] == 1)
        { 
             
            // Update all multiples of p 
            for(let i = p * 2; i <= n; i += p) 
                prime[i] = 0; 
        } 
    } 
   
    for(let i = 2; i <= n; i++)
    { 
         
        // If i is prime 
        if (prime[i] != 0)
        { 
             
            // 2p + 1 
            let temp = (2 * i) + 1; 
   
            // If 2p + 1 is also a prime 
            // then set prime[2p + 1] = 2 
            if (temp <= n && prime[temp] != 0) 
                prime[temp] = 2; 
        } 
    } 
   
    for(let i = 5; i <= n; i++) 
   
        // i is a safe prime 
        if (prime[i] == 2) 
            document.write(i + " "); 
}
 
// Driver code 
let n = 20; 
printSafePrimes(n); 
 
// This code is contributed by unknown2108
 
</script>

Output:

5 7 11

Time complexity: O(nlog(logn)) same as Sieve of Eratosthenes

Auxiliary Space: O(n), since n extra space has been taken.

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