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.