Mathematics

Print safe prime numbers from 1 to n

A safe prime number is a prime number of the form 2p+1, where both p and (2p+1) are prime numbers.

To print safe prime numbers from 1 to n, you would need to perform the following steps:

Create a loop that iterates from 2 to n, testing each number to determine if it is a prime number.
For each prime number found in step 1, test if 2p+1 (where p is the prime number) is also a prime number.
If 2p+1 is a prime number, then the number is a safe prime. Print it.

Program Solution

// Java program for
// Print safe prime numbers from 1 to n
public class PrimeNumber
{
	public void eratosthenesSieve(boolean[] prime, int n)
	{
		// Set all element as prime
		for (int i = 0; i <= n; ++i)
		{
			prime[i] = true;
		}
		prime[0] = false;
		prime[1] = false;
		for (int i = 2; i <= n; ++i)
		{
			if (prime[i] == true)
			{
				for (int j = i *i; j <= n; j += i)
				{
					prime[j] = false;
				}
			}
		}
	}
	public void printSafePrime(int n)
	{
		if (n < 1)
		{
			return;
		}
		System.out.println("\n  Given n :" + n);
		boolean[] prime = new boolean[n + 1];
		eratosthenesSieve(prime, n);
		int j = 0;
		// Print safe prime (2..n)
		for (int i = 2; i <= n; ++i)
		{
			if (prime[i] == true)
			{
				j = (i * 2) + 1;
				if (j <= n && prime[j])
				{
					System.out.print("  " + j);
				}
			}
		}
	}
	public static void main(String[] args)
	{
		PrimeNumber task = new PrimeNumber();
		// Test
		task.printSafePrime(100);
		task.printSafePrime(300);
	}
}

Output

  Given n :100
  5  7  11  23  47  59  83
  Given n :300
  5  7  11  23  47  59  83  107  167  179  227  263

// Include header file
#include <iostream>
using namespace std;
// C++ program for
// Print safe prime numbers from 1 to n
class PrimeNumber
{
	public: void eratosthenesSieve(bool prime[], int n)
	{
		// Set all element as prime
		for (int i = 0; i <= n; ++i)
		{
			prime[i] = true;
		}
		prime[0] = false;
		prime[1] = false;
		for (int i = 2; i <= n; ++i)
		{
			if (prime[i] == true)
			{
				for (int j = i *i; j <= n; j += i)
				{
					prime[j] = false;
				}
			}
		}
	}
	void printSafePrime(int n)
	{
		if (n < 1)
		{
			return;
		}
		cout << "\n  Given n :" 
             << n << endl;
		bool prime[n + 1];
		this->eratosthenesSieve(prime, n);
		int j = 0;
		// Print safe prime (2..n)
		for (int i = 2; i <= n; ++i)
		{
			if (prime[i] == true)
			{
				j = (i *2) + 1;
				if (j <= n && prime[j])
				{
					cout << "  " << j;
				}
			}
		}
	}
};
int main()
{
	PrimeNumber *task = new PrimeNumber();
	// Test
	task->printSafePrime(100);
	task->printSafePrime(300);
	return 0;
}

Output

  Given n :100
  5  7  11  23  47  59  83
  Given n :300
  5  7  11  23  47  59  83  107  167  179  227  263

// Include namespace system
using System;
// Csharp program for
// Print safe prime numbers from 1 to n
public class PrimeNumber
{
	public void eratosthenesSieve(Boolean[] prime, int n)
	{
		// Set all element as prime
		for (int i = 0; i <= n; ++i)
		{
			prime[i] = true;
		}
		prime[0] = false;
		prime[1] = false;
		for (int i = 2; i <= n; ++i)
		{
			if (prime[i] == true)
			{
				for (int j = i * i; j <= n; j += i)
				{
					prime[j] = false;
				}
			}
		}
	}
	public void printSafePrime(int n)
	{
		if (n < 1)
		{
			return;
		}
		Console.WriteLine("\n  Given n :" + n);
		Boolean[] prime = new Boolean[n + 1];
		this.eratosthenesSieve(prime, n);
		int j = 0;
		// Print safe prime (2..n)
		for (int i = 2; i <= n; ++i)
		{
			if (prime[i] == true)
			{
				j = (i * 2) + 1;
				if (j <= n && prime[j])
				{
					Console.Write("  " + j);
				}
			}
		}
	}
	public static void Main(String[] args)
	{
		PrimeNumber task = new PrimeNumber();
		// Test
		task.printSafePrime(100);
		task.printSafePrime(300);
	}
}

Output

  Given n :100
  5  7  11  23  47  59  83
  Given n :300
  5  7  11  23  47  59  83  107  167  179  227  263

package main
import "fmt"
// Go program for
// Print safe prime numbers from 1 to n

func eratosthenesSieve(prime[] bool, n int) {
	// Set all element as prime
	for i := 0 ; i <= n ; i++ {
		prime[i] = true
	}
	prime[0] = false
	prime[1] = false
	for i := 2 ; i <= n ; i++ {
		if prime[i] == true {
			for j := i * i ; j <= n ; j += i {
				prime[j] = false
			}
		}
	}
}
func printSafePrime(n int) {
	if n < 1 {
		return
	}
	fmt.Println("\n  Given n :", n)
	var prime = make([] bool, n + 1)
	eratosthenesSieve(prime, n)
	var j int = 0
	// Print safe prime (2..n)
	for i := 2 ; i <= n ; i++ {
		if prime[i] == true {
			j = (i * 2) + 1
			if j <= n && prime[j] {
				fmt.Print("  ", j)
			}
		}
	}
}
func main() {
	
	// Test
	printSafePrime(100)
	printSafePrime(300)
}

Output

  Given n :100
  5  7  11  23  47  59  83
  Given n :300
  5  7  11  23  47  59  83  107  167  179  227  263

<?php
// Php program for
// Print safe prime numbers from 1 to n
class PrimeNumber
{
	public	function eratosthenesSieve(&$prime, $n)
	{
		$prime[0] = false;
		$prime[1] = false;
		for ($i = 2; $i <= $n; ++$i)
		{
			if ($prime[$i] == true)
			{
				for ($j = $i * $i; $j <= $n; $j += $i)
				{
					$prime[$j] = false;
				}
			}
		}
	}
	public	function printSafePrime($n)
	{
		if ($n < 1)
		{
			return;
		}
		echo("\n  Given n :".$n."\n");
		// Set all element as prime
		$prime = array_fill(0, $n + 1, true);
		$this->eratosthenesSieve($prime, $n);
		$j = 0;
		// Print safe prime (2..n)
		for ($i = 2; $i <= $n; ++$i)
		{
			if ($prime[$i] == true)
			{
				$j = ($i * 2) + 1;
				if ($j <= $n && $prime[$j])
				{
					echo("  ".$j);
				}
			}
		}
	}
}

function main()
{
	$task = new PrimeNumber();
	// Test
	$task->printSafePrime(100);
	$task->printSafePrime(300);
}
main();

Output

  Given n :100
  5  7  11  23  47  59  83
  Given n :300
  5  7  11  23  47  59  83  107  167  179  227  263

// Node JS program for
// Print safe prime numbers from 1 to n
class PrimeNumber
{
	eratosthenesSieve(prime, n)
	{
		prime[0] = false;
		prime[1] = false;
		for (var i = 2; i <= n; ++i)
		{
			if (prime[i] == true)
			{
				for (var j = i * i; j <= n; j += i)
				{
					prime[j] = false;
				}
			}
		}
	}
	printSafePrime(n)
	{
		if (n < 1)
		{
			return;
		}
		console.log("\n  Given n : " + n);
		// Set all element as prime
		var prime = Array(n + 1).fill(true);
		this.eratosthenesSieve(prime, n);
		var j = 0;
		// Print safe prime (2..n)
		for (var i = 2; i <= n; ++i)
		{
			if (prime[i] == true)
			{
				j = (i * 2) + 1;
				if (j <= n && prime[j])
				{
					process.stdout.write("  " + j);
				}
			}
		}
	}
}

function main()
{
	var task = new PrimeNumber();
	// Test
	task.printSafePrime(100);
	task.printSafePrime(300);
}
main();

Output

  Given n : 100
  5  7  11  23  47  59  83
  Given n : 300
  5  7  11  23  47  59  83  107  167  179  227  263

#  Python 3 program for
#  Print safe prime numbers from 1 to n
class PrimeNumber :
	def eratosthenesSieve(self, prime, n) :
		prime[0] = False
		prime[1] = False
		i = 2
		while (i <= n) :
			if (prime[i] == True) :
				j = i * i
				while (j <= n) :
					prime[j] = False
					j += i
				
			
			i += 1
		
	
	def printSafePrime(self, n) :
		if (n < 1) :
			return
		
		print("\n  Given n :", n)
		#  Set all element as prime
		prime = [True] * (n + 1)
		self.eratosthenesSieve(prime, n)
		j = 0
		i = 2
		#  Print safe prime (2..n)
		while (i <= n) :
			if (prime[i] == True) :
				j = (i * 2) + 1
				if (j <= n and prime[j]) :
					print("  ", j, end = "")
				
			
			i += 1
		
	

def main() :
	task = PrimeNumber()
	#  Test
	task.printSafePrime(100)
	task.printSafePrime(300)

if __name__ == "__main__": main()

Output

  Given n : 100
   5   7   11   23   47   59   83
  Given n : 300
   5   7   11   23   47   59   83   107   167   179   227   263

#  Ruby program for
#  Print safe prime numbers from 1 to n
class PrimeNumber 
	def eratosthenesSieve(prime, n) 
		prime[0] = false
		prime[1] = false
		i = 2
		while (i <= n) 
			if (prime[i] == true) 
				j = i * i
				while (j <= n) 
					prime[j] = false
					j += i
				end

			end

			i += 1
		end

	end

	def printSafePrime(n) 
		if (n < 1) 
			return
		end

		print("\n  Given n :", n, "\n")
		#  Set all element as prime
		prime = Array.new(n + 1) {true}
		self.eratosthenesSieve(prime, n)
		j = 0
		i = 2
		#  Print safe prime (2..n)
		while (i <= n) 
			if (prime[i] == true) 
				j = (i * 2) + 1
				if (j <= n && prime[j]) 
					print("  ", j)
				end

			end

			i += 1
		end

	end

end

def main() 
	task = PrimeNumber.new()
	#  Test
	task.printSafePrime(100)
	task.printSafePrime(300)
end

main()

Output

  Given n :100
  5  7  11  23  47  59  83
  Given n :300
  5  7  11  23  47  59  83  107  167  179  227  263

// Scala program for
// Print safe prime numbers from 1 to n
class PrimeNumber()
{
	def eratosthenesSieve(prime: Array[Boolean], n: Int): Unit = {
		prime(0) = false;
		prime(1) = false;
		var i: Int = 2;
		while (i <= n)
		{
			if (prime(i) == true)
			{
				var j: Int = i * i;
				while (j <= n)
				{
					prime(j) = false;
					j += i;
				}
			}
			i += 1;
		}
	}
	def printSafePrime(n: Int): Unit = {
		if (n < 1)
		{
			return;
		}
		println("\n  Given n :" + n);
		// Set all element as prime
		var prime: Array[Boolean] = Array.fill[Boolean](n + 1)(true);
		eratosthenesSieve(prime, n);
		var j: Int = 0;
		var i: Int = 2;
		// Print safe prime (2..n)
		while (i <= n)
		{
			if (prime(i) == true)
			{
				j = (i * 2) + 1;
				if (j <= n && prime(j))
				{
					print("  " + j);
				}
			}
			i += 1;
		}
	}
}
object Main
{
	def main(args: Array[String]): Unit = {
		var task: PrimeNumber = new PrimeNumber();
		// Test
		task.printSafePrime(100);
		task.printSafePrime(300);
	}
}

Output

  Given n :100
  5  7  11  23  47  59  83
  Given n :300
  5  7  11  23  47  59  83  107  167  179  227  263

// Swift 4 program for
// Print safe prime numbers from 1 to n
class PrimeNumber
{
	func eratosthenesSieve(_ prime: inout[Bool], _ n: Int)
	{
		prime[0] = false;
		prime[1] = false;
		var i: Int = 2;
		while (i <= n)
		{
			if (prime[i] == true)
			{
				var j: Int = i * i;
				while (j <= n)
				{
					prime[j] = false;
					j += i;
				}
			}
			i += 1;
		}
	}
	func printSafePrime(_ n: Int)
	{
		if (n < 1)
		{
			return;
		}
		print("\n  Given n :", n);
		// Set all element as prime
		var prime: [Bool] = Array(repeating: true, count: n + 1);
		self.eratosthenesSieve(&prime, n);
		var j: Int = 0;
		var i: Int = 2;
		// Print safe prime (2..n)
		while (i <= n)
		{
			if (prime[i] == true)
			{
				j = (i * 2) + 1;
				if (j <= n && prime[j])
				{
					print("  ", j, terminator: "");
				}
			}
			i += 1;
		}
	}
}
func main()
{
	let task: PrimeNumber = PrimeNumber();
	// Test
	task.printSafePrime(100);
	task.printSafePrime(300);
}
main();

Output

  Given n : 100
   5   7   11   23   47   59   83
  Given n : 300
   5   7   11   23   47   59   83   107   167   179   227   263

// Kotlin program for
// Print safe prime numbers from 1 to n
class PrimeNumber
{
	fun eratosthenesSieve(prime: Array < Boolean > , n: Int): Unit
	{
		prime[0] = false;
		prime[1] = false;
		var i: Int = 2;
		while (i <= n)
		{
			if (prime[i] == true)
			{
				var j: Int = i * i;
				while (j <= n)
				{
					prime[j] = false;
					j += i;
				}
			}
			i += 1;
		}
	}
	fun printSafePrime(n: Int): Unit
	{
		if (n < 1)
		{
			return;
		}
		println("\n  Given n :" + n);
		// Set all element as prime
		var prime: Array < Boolean > = Array(n + 1)
		{
			true
		};
		this.eratosthenesSieve(prime, n);
		var j: Int;
		var i: Int = 2;
		// Print safe prime (2..n)
		while (i <= n)
		{
			if (prime[i] == true)
			{
				j = (i * 2) + 1;
				if (j <= n && prime[j])
				{
					print("  " + j);
				}
			}
			i += 1;
		}
	}
}
fun main(args: Array < String > ): Unit
{
	val task: PrimeNumber = PrimeNumber();
	// Test
	task.printSafePrime(100);
	task.printSafePrime(300);
}

Output

  Given n :100
  5  7  11  23  47  59  83
  Given n :300
  5  7  11  23  47  59  83  107  167  179  227  263

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