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++ 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 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 |
# 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# 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 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 ?> |
<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> |
5 7 11
Time complexity: O(nlog(logn)) same as Sieve of Eratosthenes
Auxiliary Space: O(n), since n extra space has been taken.