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 + 1Input: 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 primesvoid 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 codeint 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 approachfrom math import sqrt# Function to print first n safe primesdef 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 codeif __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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