# Bitwise Sieve

Here given code implementation process.

``````// C Program
// Print Prime numbers using
// Bitwise Sieve
#include <stdio.h>

int non_prime(int num, int position)
{
return (num & (1 << position));
}
int update_status(int num, int position)
{
return (num | (1 << position));
}
//Find all prime numbers which have smaller and equal to given number n
void bitwise_sieve(int n)
{
if (n <= 1)
{
//When n are invalid to prime number
return;
}
int space = (n >> 5) + 2;
//This are used to detect prime numbers
int sieve[space];
// Loop controlling variables
int i = 0;
int j = 0;
//define some auxiliary variable
int slot = 0;
int position = 0;
for (i = 3; i * i <= n; i = i + 2)
{
//get slot and position
slot = i >> 5;
position = i & 31;
if (non_prime(sieve[slot], position) == 0)
{
for (j = i * i; j <= n; j += (i << 1))
{
//get slot and position
slot = j >> 5;
position = j & 31;
sieve[slot] = update_status(sieve[slot], position);
}
}
}
printf("\n Prime of (2 - %d) are \n", n);
//Display first element
printf(" [ 2");
for (i = 3; i <= n; i = i + 2)
{
//get slot and position
slot = i >> 5;
position = i & 31;
if (non_prime(sieve[slot], position) == 0)
{
//When [i] is a prime number
printf("  %d", i);
}
}
printf(" ] \n");
}
int main()
{
bitwise_sieve(25);
bitwise_sieve(101);
bitwise_sieve(200);
return 0;
}``````

#### Output

`````` Prime of (2 - 25) are
[ 2  3  5  7  11  13  17  19  23 ]

Prime of (2 - 101) are
[ 2  3  11  13  17  19  23  25  29  31  35  37  41  43  47  49  53  55  59  61  67  77  79  83  85  89  91  95  97  101 ]

Prime of (2 - 200) are
[ 2  3  11  13  17  19  23  25  29  31  35  37  41  43  47  49  53  55  59  61  67  77  79  83  85  89  91  95  97  101  103  107  109  113  115  119  125  127  131  139  145  151  157  163  175  181 ]``````
``````// Java Program
// Print prime number by using
// Bitwise Sieve
class BitwiseSieve
{
public int non_prime(int num, int position)
{
return (num & (1 << position));
}
public int update_status(int num, int position)
{
return (num | (1 << position));
}
//Find all prime numbers which have smaller and equal to given number n
public void bitwise_sieve(int n)
{
if (n <= 1)
{
//When n are invalid to prime number
return;
}
int space = (n >> 5) + 2;
//This are used to detect prime numbers
int[] sieve = new int[space];
// Loop controlling variables
int i = 0;
int j = 0;
//define some auxiliary variable
int slot = 0;
int position = 0;
for (i = 3; i * i <= n; i = i + 2)
{
//get slot and position
slot = i >> 5;
position = i & 31;
if (non_prime(sieve[slot], position) == 0)
{
for (j = i * i; j <= n; j += (i << 1))
{
//get slot and position
slot = j >> 5;
position = j & 31;
sieve[slot] = update_status(sieve[slot], position);
}
}
}
System.out.print("\n Prime of (2 - " + n + ") are \n");
//Display first element
System.out.print(" [ 2");
for (i = 3; i <= n; i = i + 2)
{
//get slot and position
slot = i >> 5;
position = i & 31;
if (non_prime(sieve[slot], position) == 0)
{
//When [i] is a prime number
System.out.print("  " + i);
}
}
System.out.print(" ] \n");
}
public static void main(String[] args)
{
BitwiseSieve obj = new BitwiseSieve();
//Test Case
obj.bitwise_sieve(25);
obj.bitwise_sieve(101);
obj.bitwise_sieve(200);
}
}``````

#### Output

`````` Prime of (2 - 25) are
[ 2  3  5  7  11  13  17  19  23 ]

Prime of (2 - 101) are
[ 2  3  5  7  11  13  17  19  23  29  31  37  41  43  47  53  59  61  67  71  73  79  83  89  97  101 ]

Prime of (2 - 200) are
[ 2  3  5  7  11  13  17  19  23  29  31  37  41  43  47  53  59  61  67  71  73  79  83  89  97  101  103  107  109  113  127  131  137  139  149  151  157  163  167  173  179  181  191  193  197  199 ]``````
``````//Include header file
#include <iostream>
using namespace std;

// C++ Program
// Print prime number by using
// Bitwise Sieve

class BitwiseSieve
{
public:
int non_prime(int num, int position)
{
return (num & (1 << position));
}
int update_status(int num, int position)
{
return (num | (1 << position));
}
//Find all prime numbers which have smaller and equal to given number n
void bitwise_sieve(int n)
{
if (n <= 1)
{
//When n are invalid to prime number
return;
}
int space = (n >> 5) + 2;
//This are used to detect prime numbers
int sieve[space];
// Loop controlling variables
int i = 0;
int j = 0;
//define some auxiliary variable
int slot = 0;
int position = 0;
for (i = 3; i *i <= n; i = i + 2)
{
//get slot and position
slot = i >> 5;
position = i & 31;
if (this->non_prime(sieve[slot], position) == 0)
{
for (j = i *i; j <= n; j += (i << 1))
{
//get slot and position
slot = j >> 5;
position = j & 31;
sieve[slot] = this->update_status(sieve[slot], position);
}
}
}
cout << "\n Prime of (2 - " << n << ") are \n";
//Display first element
cout << " [ 2";
for (i = 3; i <= n; i = i + 2)
{
//get slot and position
slot = i >> 5;
position = i & 31;
if (this->non_prime(sieve[slot], position) == 0)
{
//When [i] is a prime number
cout << "  " << i;
}
}
cout << " ] \n";
}
};
int main()
{
BitwiseSieve obj = BitwiseSieve();
//Test Case
obj.bitwise_sieve(25);
obj.bitwise_sieve(101);
obj.bitwise_sieve(200);
return 0;
}``````

#### Output

`````` Prime of (2 - 25) are
[ 2  3  5  7  11  13  17  19  23 ]

Prime of (2 - 101) are
[ 2  3  7  11  13  23  29  47  53  55  59  61  67  71  79  83  85  89  95  97  101 ]

Prime of (2 - 200) are
[ 2  3  7  11  13  23  29  47  53  55  59  61  67  71  79  83  85  89  95  97  101  103  107  109  113  115  125  127  131  139  151  157  181  199 ]``````
``````//Include namespace system
using System;

// C# Program
// Print prime number by using
// Bitwise Sieve

class BitwiseSieve
{
public int non_prime(int num, int position)
{
return (num & (1 << position));
}
public int update_status(int num, int position)
{
return (num | (1 << position));
}
//Find all prime numbers which have smaller and equal to given number n
public void bitwise_sieve(int n)
{
if (n <= 1)
{
//When n are invalid to prime number
return;
}
int space = (n >> 5) + 2;
//This are used to detect prime numbers
int[] sieve = new int[space];
// Loop controlling variables
int i = 0;
int j = 0;
//define some auxiliary variable
int slot = 0;
int position = 0;
for (i = 3; i * i <= n; i = i + 2)
{
//get slot and position
slot = i >> 5;
position = i & 31;
if (non_prime(sieve[slot], position) == 0)
{
for (j = i * i; j <= n; j += (i << 1))
{
//get slot and position
slot = j >> 5;
position = j & 31;
sieve[slot] = update_status(sieve[slot], position);
}
}
}
Console.Write("\n Prime of (2 - " + n + ") are \n");
//Display first element
Console.Write(" [ 2");
for (i = 3; i <= n; i = i + 2)
{
//get slot and position
slot = i >> 5;
position = i & 31;
if (non_prime(sieve[slot], position) == 0)
{
//When [i] is a prime number
Console.Write("  " + i);
}
}
Console.Write(" ] \n");
}
public static void Main(String[] args)
{
BitwiseSieve obj = new BitwiseSieve();
//Test Case
obj.bitwise_sieve(25);
obj.bitwise_sieve(101);
obj.bitwise_sieve(200);
}
}``````

#### Output

`````` Prime of (2 - 25) are
[ 2  3  5  7  11  13  17  19  23 ]

Prime of (2 - 101) are
[ 2  3  5  7  11  13  17  19  23  29  31  37  41  43  47  53  59  61  67  71  73  79  83  89  97  101 ]

Prime of (2 - 200) are
[ 2  3  5  7  11  13  17  19  23  29  31  37  41  43  47  53  59  61  67  71  73  79  83  89  97  101  103  107  109  113  127  131  137  139  149  151  157  163  167  173  179  181  191  193  197  199 ]``````
``````<?php
// Php Program
// Print prime number by using
// Bitwise Sieve

class BitwiseSieve
{
public	function non_prime(\$num, \$position)
{
return (\$num & (1 << \$position));
}
public	function update_status(\$num, \$position)
{
return (\$num | (1 << \$position));
}
//Find all prime numbers which have smaller and equal to given number n
public	function bitwise_sieve(\$n)
{
if (\$n <= 1)
{
//When n are invalid to prime number
return;
}
\$space = (\$n >> 5) + 2;
//This are used to detect prime numbers
\$sieve = array_fill(0, \$space, 0);
// Loop controlling variables
\$i = 0;
\$j = 0;
//define some auxiliary variable
\$slot = 0;
\$position = 0;
for (\$i = 3; \$i * \$i <= \$n; \$i = \$i + 2)
{
//get slot and position
\$slot = \$i >> 5;
\$position = \$i & 31;
if (\$this->non_prime(\$sieve[\$slot], \$position) == 0)
{
for (\$j = \$i * \$i; \$j <= \$n; \$j += (\$i << 1))
{
//get slot and position
\$slot = \$j >> 5;
\$position = \$j & 31;
\$sieve[\$slot] = \$this->update_status(\$sieve[\$slot], \$position);
}
}
}
echo "\n Prime of (2 - ". \$n .") are \n";
//Display first element
echo " [ 2";
for (\$i = 3; \$i <= \$n; \$i = \$i + 2)
{
//get slot and position
\$slot = \$i >> 5;
\$position = \$i & 31;
if (\$this->non_prime(\$sieve[\$slot], \$position) == 0)
{
//When [i] is a prime number
echo "  ". \$i;
}
}
echo " ] \n";
}
}

function main()
{
\$obj = new BitwiseSieve();
//Test Case
\$obj->bitwise_sieve(25);
\$obj->bitwise_sieve(101);
\$obj->bitwise_sieve(200);
}
main();``````

#### Output

`````` Prime of (2 - 25) are
[ 2  3  5  7  11  13  17  19  23 ]

Prime of (2 - 101) are
[ 2  3  5  7  11  13  17  19  23  29  31  37  41  43  47  53  59  61  67  71  73  79  83  89  97  101 ]

Prime of (2 - 200) are
[ 2  3  5  7  11  13  17  19  23  29  31  37  41  43  47  53  59  61  67  71  73  79  83  89  97  101  103  107  109  113  127  131  137  139  149  151  157  163  167  173  179  181  191  193  197  199 ]``````
``````// Node Js Program
// Print prime number by using
// Bitwise Sieve

class BitwiseSieve
{
non_prime(num, position)
{
return (num & (1 << position));
}
update_status(num, position)
{
return (num | (1 << position));
}
//Find all prime numbers which have smaller and equal to given number n
bitwise_sieve(n)
{
if (n <= 1)
{
//When n are invalid to prime number
return;
}
var space = (n >> 5) + 2;
//This are used to detect prime numbers
var sieve = Array(space).fill(0);
// Loop controlling variables
var i = 0;
var j = 0;
//define some auxiliary variable
var slot = 0;
var position = 0;
for (i = 3; i * i <= n; i = i + 2)
{
//get slot and position
slot = i >> 5;
position = i & 31;
if (this.non_prime(sieve[slot], position) == 0)
{
for (j = i * i; j <= n; j += (i << 1))
{
//get slot and position
slot = j >> 5;
position = j & 31;
sieve[slot] = this.update_status(sieve[slot], position);
}
}
}
process.stdout.write("\n Prime of (2 - " + n + ") are \n");
//Display first element
process.stdout.write(" [ 2");
for (i = 3; i <= n; i = i + 2)
{
//get slot and position
slot = i >> 5;
position = i & 31;
if (this.non_prime(sieve[slot], position) == 0)
{
//When [i] is a prime number
process.stdout.write("  " + i);
}
}
process.stdout.write(" ] \n");
}
}

function main()
{
var obj = new BitwiseSieve();
//Test Case
obj.bitwise_sieve(25);
obj.bitwise_sieve(101);
obj.bitwise_sieve(200);
}
main();``````

#### Output

`````` Prime of (2 - 25) are
[ 2  3  5  7  11  13  17  19  23 ]

Prime of (2 - 101) are
[ 2  3  5  7  11  13  17  19  23  29  31  37  41  43  47  53  59  61  67  71  73  79  83  89  97  101 ]

Prime of (2 - 200) are
[ 2  3  5  7  11  13  17  19  23  29  31  37  41  43  47  53  59  61  67  71  73  79  83  89  97  101  103  107  109  113  127  131  137  139  149  151  157  163  167  173  179  181  191  193  197  199 ]``````
``````#  Python 3 Program
#  Print prime number by using
#  Bitwise Sieve

class BitwiseSieve :
def non_prime(self, num, position) :
return (num & (1 << position))

def update_status(self, num, position) :
return (num | (1 << position))

# Find all prime numbers which have smaller and equal to given number n
def bitwise_sieve(self, n) :
if (n <= 1) :
# When n are invalid to prime number
return

space = (n >> 5) + 2
# This are used to detect prime numbers
sieve = [0] * space
# define some auxiliary variable
slot = 0
position = 0
#  Loop controlling variables
i = 3
j = 0
while (i * i <= n) :
# get slot and position
slot = i >> 5
position = i & 31
if (self.non_prime(sieve[slot], position) == 0) :
j = i * i
while (j <= n) :
# get slot and position
slot = j >> 5
position = j & 31
sieve[slot] = self.update_status(sieve[slot], position)
j += (i << 1)

i = i + 2

print("\n Prime of (2 - ", n ,") are \n", end = "")
# Display first element
print(" [ 2", end = "")
i = 3
while (i <= n) :
# get slot and position
slot = i >> 5
position = i & 31
if (self.non_prime(sieve[slot], position) == 0) :
# When [i] is a prime number
print("  ", i, end = "")

i = i + 2

print(" ] \n", end = "")

def main() :
obj = BitwiseSieve()
# Test Case
obj.bitwise_sieve(25)
obj.bitwise_sieve(101)
obj.bitwise_sieve(200)

if __name__ == "__main__": main()``````

#### Output

`````` Prime of (2 -  25 ) are
[ 2   3   5   7   11   13   17   19   23 ]

Prime of (2 -  101 ) are
[ 2   3   5   7   11   13   17   19   23   29   31   37   41   43   47   53   59   61   67   71   73   79   83   89   97   101 ]

Prime of (2 -  200 ) are
[ 2   3   5   7   11   13   17   19   23   29   31   37   41   43   47   53   59   61   67   71   73   79   83   89   97   101   103   107   109   113   127   131   137   139   149   151   157   163   167   173   179   181   191   193   197   199 ]``````
``````#  Ruby Program
#  Print prime number by using
#  Bitwise Sieve
class BitwiseSieve

def non_prime(num, position)
return (num & (1 << position))
end
def update_status(num, position)

return (num | (1 << position))
end
# Find all prime numbers which have smaller and equal to given number n
def bitwise_sieve(n)

if (n <= 1)
# When n are invalid to prime number
return
end
space = (n >> 5) + 2
# This are used to detect prime numbers
sieve = Array.new(space) {0}
# define some auxiliary variable
slot = 0
position = 0
#  Loop controlling variables
i = 3
j = 0
while (i * i <= n)

# get slot and position
slot = i >> 5
position = i & 31
if (self.non_prime(sieve[slot], position) == 0)

j = i * i
while (j <= n)

# get slot and position
slot = j >> 5
position = j & 31
sieve[slot] = self.update_status(sieve[slot], position)
j += (i << 1)
end
end
i = i + 2
end
print("\n Prime of (2 - ", n ,") are \n")
# Display first element
print(" [ 2")
i = 3
while (i <= n)

# get slot and position
slot = i >> 5
position = i & 31
if (self.non_prime(sieve[slot], position) == 0)

# When [i] is a prime number
print("  ", i)
end
i = i + 2
end
print(" ] \n")
end
end
def main()

obj = BitwiseSieve.new()
# Test Case
obj.bitwise_sieve(25)
obj.bitwise_sieve(101)
obj.bitwise_sieve(200)
end
main()``````

#### Output

`````` Prime of (2 - 25) are
[ 2  3  5  7  11  13  17  19  23 ]

Prime of (2 - 101) are
[ 2  3  5  7  11  13  17  19  23  29  31  37  41  43  47  53  59  61  67  71  73  79  83  89  97  101 ]

Prime of (2 - 200) are
[ 2  3  5  7  11  13  17  19  23  29  31  37  41  43  47  53  59  61  67  71  73  79  83  89  97  101  103  107  109  113  127  131  137  139  149  151  157  163  167  173  179  181  191  193  197  199 ]
``````
``````// Scala Program
// Print prime number by using
// Bitwise Sieve
class BitwiseSieve
{
def non_prime(num: Int, position: Int): Int = {
return (num & (1 << position));
}
def update_status(num: Int, position: Int): Int = {
return (num | (1 << position));
}
//Find all prime numbers which have smaller and equal to given number n
def bitwise_sieve(n: Int): Unit = {
if (n <= 1)
{
//When n are invalid to prime number
return;
}
var space: Int = (n >> 5) + 2;
//This are used to detect prime numbers
var sieve: Array[Int] = Array.fill[Int](space)(0);
//define some auxiliary variable
var slot: Int = 0;
var position: Int = 0;
// Loop controlling variables
var i: Int = 3;
var j: Int = 0;
while (i * i <= n)
{
//get slot and position
slot = i >> 5;
position = i & 31;
if (non_prime(sieve(slot), position) == 0)
{
j = i * i;
while (j <= n)
{
//get slot and position
slot = j >> 5;
position = j & 31;
sieve(slot) = update_status(sieve(slot), position);
j += (i << 1);
}
}
i = i + 2;
}
print("\n Prime of (2 - " + n + ") are \n");
//Display first element
print(" [ 2");
i = 3;
while (i <= n)
{
//get slot and position
slot = i >> 5;
position = i & 31;
if (non_prime(sieve(slot), position) == 0)
{
//When [i] is a prime number
print("  " + i);
}
i = i + 2;
}
print(" ] \n");
}
}
object Main
{
def main(args: Array[String]): Unit = {
var obj: BitwiseSieve = new BitwiseSieve();
//Test Case
obj.bitwise_sieve(25);
obj.bitwise_sieve(101);
obj.bitwise_sieve(200);
}
}``````

#### Output

`````` Prime of (2 - 25) are
[ 2  3  5  7  11  13  17  19  23 ]

Prime of (2 - 101) are
[ 2  3  5  7  11  13  17  19  23  29  31  37  41  43  47  53  59  61  67  71  73  79  83  89  97  101 ]

Prime of (2 - 200) are
[ 2  3  5  7  11  13  17  19  23  29  31  37  41  43  47  53  59  61  67  71  73  79  83  89  97  101  103  107  109  113  127  131  137  139  149  151  157  163  167  173  179  181  191  193  197  199 ]``````
``````// Swift Program
// Print prime number by using
// Bitwise Sieve
class BitwiseSieve
{
func non_prime(_ num: Int, _ position: Int) -> Int
{
return (num & (1 << position));
}
func update_status(_ num: Int, _ position: Int) -> Int
{
return (num | (1 << position));
}
//Find all prime numbers which have smaller and equal to given number n
func bitwise_sieve(_ n: Int)
{
if (n <= 1)
{
//When n are invalid to prime number
return;
}
let space: Int = (n >> 5) + 2;
//This are used to detect prime numbers
var sieve: [Int] = Array(repeating: 0, count: space);
//define some auxiliary variable
var slot: Int = 0;
var position: Int = 0;
// Loop controlling variables
var i: Int = 3;
var j: Int = 0;
while (i * i <= n)
{
//get slot and position
slot = i >> 5;
position = i & 31;
if (self.non_prime(sieve[slot], position) == 0)
{
j = i * i;
while (j <= n)
{
//get slot and position
slot = j >> 5;
position = j & 31;
sieve[slot] = self.update_status(sieve[slot], position);
j += (i << 1);
}
}
i = i + 2;
}
print("\n Prime of (2 - ", n ,") are \n", terminator: "");
//Display first element
print(" [ 2", terminator: "");
i = 3;
while (i <= n)
{
//get slot and position
slot = i >> 5;
position = i & 31;
if (self.non_prime(sieve[slot], position) == 0)
{
//When [i] is a prime number
print("  ", i, terminator: "");
}
i = i + 2;
}
print(" ] \n", terminator: "");
}
}
func main()
{
let obj: BitwiseSieve = BitwiseSieve();
//Test Case
obj.bitwise_sieve(25);
obj.bitwise_sieve(101);
obj.bitwise_sieve(200);
}
main();``````

#### Output

`````` Prime of (2 -  25 ) are
[ 2   3   5   7   11   13   17   19   23 ]

Prime of (2 -  101 ) are
[ 2   3   5   7   11   13   17   19   23   29   31   37   41   43   47   53   59   61   67   71   73   79   83   89   97   101 ]

Prime of (2 -  200 ) are
[ 2   3   5   7   11   13   17   19   23   29   31   37   41   43   47   53   59   61   67   71   73   79   83   89   97   101   103   107   109   113   127   131   137   139   149   151   157   163   167   173   179   181   191   193   197   199 ]``````

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