# Sieve of Atkin

Here given code implementation process.

``````// C Program
// Print prime number by using
// Sieve of Atkin
#include <stdio.h>

//Find all prime numbers which have smaller and equal to given number n
void sieve_of_atkin(int n)
{
if (n <= 1)
{
//When n are invalid to prime number
return;
}
//this are used to detect prime numbers
int sieve[n + 1];
// Loop controlling variables
int x = 0;
int y = 0;
//used to get calculated result
int num = 0;
//Set initial all the numbers are non prime
for (x = 0; x <= n; ++x)
{
sieve[x] = 0;
}
for (x = 1; x * x < n; ++x)
{
for (y = 1; y * y < n; ++y)
{
//Calculate 4x²+y²
num = (4 * x * x) + (y * y);
if (num <= n && (num % 12 == 1 || num % 12 == 5))
{
sieve[num] = sieve[num] ^ 1;
}
//Calculate 3x²+y²
num = (3 * x * x) + (y * y);
if (num <= n && num % 12 == 7)
{
sieve[num] = sieve[num] ^ 1;
}
//Calculate 3x²+y²
num = (3 * x * x) - (y * y);
if (x > y && num <= n && num % 12 == 11)
{
sieve[num] = sieve[num] ^ 1;
}
}
}
for (x = 5; x * x <= n; x++)
{
if (sieve[x] == 1)
{
// When x is prime
// Set multiples of squares as non-prime
for (y = x * x; y <= n; y += x * x)
{
sieve[y] = 0;
}
}
}
//set initial 2 prime value
if (n >= 2)
{
//set 2 is prime
sieve[2] = 1;
}
if (n >= 3)
{
//set 3 is prime
sieve[3] = 1;
}
printf("\n All prime of (2 - %d) is :  \n [", n);
//Display prime element
for (x = 0; x <= n; ++x)
{
if (sieve[x] == 1)
{
printf("  %d", x);
}
}
printf("  ]\n");
}
int main()
{
//Test Case
sieve_of_atkin(25);
sieve_of_atkin(100);
sieve_of_atkin(200);
return 0;
}``````

#### Output

`````` All prime of (2 - 25) is :
[  2  3  5  7  11  13  17  19  23  ]

All prime of (2 - 100) is :
[  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  ]

All prime of (2 - 200) is :
[  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  ]``````
``````// Java Program
// Print prime number by using
// Sieve of Atkin
class SieveOfAtkin
{
//Find all prime numbers which have smaller and equal to given number n
public void sieve_of_atkin(int n)
{
if (n <= 1)
{
//When n are invalid to prime number
return;
}
//This are used to detect prime numbers
boolean[] sieve = new boolean[n + 1];
// Loop controlling variables
int x = 0;
int y = 0;
//used to get calculated result
int num = 0;
//Set initial all the numbers are non prime
for (x = 0; x <= n; ++x)
{
sieve[x] = false;
}
for (x = 1;
(x * x) < n; ++x)
{
for (y = 1; y * y < n; ++y)
{
//Calculate 4x²+y²
num = (4 * x * x) + (y * y);
if (num <= n && (num % 12 == 1 || num % 12 == 5))
{
sieve[num] = sieve[num] ^ true;
}
//Calculate 3x²+y²
num = (3 * x * x) + (y * y);
if (num <= n && num % 12 == 7)
{
sieve[num] = sieve[num] ^ true;
}
//Calculate 3x²+y²
num = (3 * x * x) - (y * y);
if (x > y && num <= n && num % 12 == 11)
{
sieve[num] = sieve[num] ^ true;
}
}
}
for (x = 5; x * x <= n; x++)
{
if (sieve[x] == true)
{
// When x is prime
// Set multiples of squares as non-prime
for (y = x * x; y <= n; y += x * x)
{
sieve[y] = false;
}
}
}
//set initial 2 prime value
if (n >= 2)
{
//set 2 is prime
sieve[2] = true;
}
if (n >= 3)
{
//set 3 is prime
sieve[3] = true;
}
System.out.print("\n All prime of (2 - " + n + ") is is : \n [");
//Display prime element
for (x = 0; x <= n; ++x)
{
if (sieve[x] == true)
{
System.out.print(" " + x);
}
}
System.out.print(" ]\n");
}
public static void main(String[] args)
{
SieveOfAtkin obj = new SieveOfAtkin();
//Test Case
obj.sieve_of_atkin(25);
obj.sieve_of_atkin(100);
obj.sieve_of_atkin(200);
}
}``````

#### Output

`````` All prime of (2 - 25) is is :
[ 2 3 5 7 11 13 17 19 23 ]

All prime of (2 - 100) is is :
[ 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 ]

All prime of (2 - 200) is is :
[ 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
// Sieve of Atkin

class SieveOfAtkin
{
public:
//Find all prime numbers which have smaller and equal to given number n
void sieve_of_atkin(int n)
{
if (n <= 1)
{
//When n are invalid to prime number
return;
}
//This are used to detect prime numbers
bool sieve[n + 1];
// Loop controlling variables
int x = 0;
int y = 0;
//used to get calculated result
int num = 0;
//Set initial all the numbers are non prime
for (x = 0; x <= n; ++x)
{
sieve[x] = false;
}
for (x = 1;
(x *x) < n; ++x)
{
for (y = 1; y * y < n; ++y)
{
//Calculate 4x²+y²
num = (4 * x * x) + (y * y);
if (num <= n && (num % 12 == 1 || num % 12 == 5))
{
sieve[num] = sieve[num] ^ true;
}
//Calculate 3x²+y²
num = (3 * x * x) + (y * y);
if (num <= n && num % 12 == 7)
{
sieve[num] = sieve[num] ^ true;
}
//Calculate 3x²+y²
num = (3 * x * x) - (y * y);
if (x > y && num <= n && num % 12 == 11)
{
sieve[num] = sieve[num] ^ true;
}
}
}
for (x = 5; (x * x) <= n; x++)
{
if (sieve[x] == true)
{
// When x is prime
// Set multiples of squares as non-prime
for (y = (x * x); y <= n; y += (x * x))
{
sieve[y] = false;
}
}
}
//set initial 2 prime value
if (n >= 2)
{
//set 2 is prime
sieve[2] = true;
}
if (n >= 3)
{
//set 3 is prime
sieve[3] = true;
}
cout << "\n All prime of (2 - " << n << ") is is : \n [";
//Display prime element
for (x = 0; x <= n; ++x)
{
if (sieve[x] == true)
{
cout << " " << x;
}
}
cout << " ]\n";
}
};
int main()
{
SieveOfAtkin obj = SieveOfAtkin();
//Test Case
obj.sieve_of_atkin(25);
obj.sieve_of_atkin(100);
obj.sieve_of_atkin(200);
return 0;
}``````

#### Output

`````` All prime of (2 - 25) is is :
[ 2 3 5 7 11 13 17 19 23 ]

All prime of (2 - 100) is is :
[ 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 ]

All prime of (2 - 200) is is :
[ 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 namespace system
using System;

// C# Program
// Print prime number by using
// Sieve of Atkin

class SieveOfAtkin
{
//Find all prime numbers which have smaller and equal to given number n
public void sieve_of_atkin(int n)
{
if (n <= 1)
{
//When n are invalid to prime number
return;
}
//This are used to detect prime numbers
Boolean[] sieve = new Boolean[n + 1];
// Loop controlling variables
int x = 0;
int y = 0;
//used to get calculated result
int num = 0;
//Set initial all the numbers are non prime
for (x = 0; x <= n; ++x)
{
sieve[x] = false;
}
for (x = 1;
(x * x) < n; ++x)
{
for (y = 1; y * y < n; ++y)
{
//Calculate 4x²+y²
num = (4 * x * x) + (y * y);
if (num <= n && (num % 12 == 1 || num % 12 == 5))
{
sieve[num] = sieve[num] ^ true;
}
//Calculate 3x²+y²
num = (3 * x * x) + (y * y);
if (num <= n && num % 12 == 7)
{
sieve[num] = sieve[num] ^ true;
}
//Calculate 3x²+y²
num = (3 * x * x) - (y * y);
if (x > y && num <= n && num % 12 == 11)
{
sieve[num] = sieve[num] ^ true;
}
}
}
for (x = 5; x * x <= n; x++)
{
if (sieve[x] == true)
{
// When x is prime
// Set multiples of squares as non-prime
for (y = x * x; y <= n; y += x * x)
{
sieve[y] = false;
}
}
}
//set initial 2 prime value
if (n >= 2)
{
//set 2 is prime
sieve[2] = true;
}
if (n >= 3)
{
//set 3 is prime
sieve[3] = true;
}
Console.Write("\n All prime of (2 - " + n + ") is is : \n [");
//Display prime element
for (x = 0; x <= n; ++x)
{
if (sieve[x] == true)
{
Console.Write("  " + x);
}
}
Console.Write(" ]\n");
}
public static void Main(String[] args)
{
SieveOfAtkin obj = new SieveOfAtkin();
//Test Case
obj.sieve_of_atkin(25);
obj.sieve_of_atkin(100);
obj.sieve_of_atkin(200);
}
}``````

#### Output

`````` All prime of (2 - 25) is is :
[  2  3  5  7  11  13  17  19  23 ]

All prime of (2 - 100) is is :
[  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 ]

All prime of (2 - 200) is is :
[  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
// Sieve of Atkin

class SieveOfAtkin
{
//Find all prime numbers which have smaller and equal to given number n
public	function sieve_of_atkin(\$n)
{
if (\$n <= 1)
{
//When n are invalid to prime number
return;
}
//This are used to detect prime numbers
//Set initial all the numbers are non prime
\$sieve = array_fill(0, \$n + 1, false);
// Loop controlling variables
\$x = 0;
\$y = 0;
//used to get calculated result
\$num = 0;
for (\$x = 1;
(\$x * \$x) < \$n; ++\$x)
{
for (\$y = 1; \$y * \$y < \$n; ++\$y)
{
//Calculate 4x²+y²
\$num = (4 * \$x * \$x) + (\$y * \$y);
if (\$num <= \$n && (\$num % 12 == 1 || \$num % 12 == 5))
{
\$sieve[\$num] = \$sieve[\$num] ^ true;
}
//Calculate 3x²+y²
\$num = (3 * \$x * \$x) + (\$y * \$y);
if (\$num <= \$n && \$num % 12 == 7)
{
\$sieve[\$num] = \$sieve[\$num] ^ true;
}
//Calculate 3x²+y²
\$num = (3 * \$x * \$x) - (\$y * \$y);
if (\$x > \$y && \$num <= \$n && \$num % 12 == 11)
{
\$sieve[\$num] = \$sieve[\$num] ^ true;
}
}
}
for (\$x = 5; \$x * \$x <= \$n; \$x++)
{
if (\$sieve[\$x] == true)
{
// When x is prime
// Set multiples of squares as non-prime
for (\$y = \$x * \$x; \$y <= \$n; \$y += \$x * \$x)
{
\$sieve[\$y] = false;
}
}
}
//set initial 2 prime value
if (\$n >= 2)
{
//set 2 is prime
\$sieve[2] = true;
}
if (\$n >= 3)
{
//set 3 is prime
\$sieve[3] = true;
}
echo "\n All prime of (2 - ". \$n .") is is : \n [";
//Display prime element
for (\$x = 0; \$x <= \$n; ++\$x)
{
if (\$sieve[\$x] == true)
{
echo "  ". \$x;
}
}
echo " ]\n";
}
}

function main()
{
\$obj = new SieveOfAtkin();
//Test Case
\$obj->sieve_of_atkin(25);
\$obj->sieve_of_atkin(100);
\$obj->sieve_of_atkin(200);
}
main();``````

#### Output

`````` All prime of (2 - 25) is is :
[  2  3  5  7  11  13  17  19  23 ]

All prime of (2 - 100) is is :
[  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 ]

All prime of (2 - 200) is is :
[  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
// Sieve of Atkin
class SieveOfAtkin
{
//Find all prime numbers which have smaller and equal to given number n
sieve_of_atkin(n)
{
if (n <= 1)
{
//When n are invalid to prime number
return;
}
//This are used to detect prime numbers
//Set initial all the numbers are non prime
var sieve = Array(n + 1).fill(false);
// Loop controlling variables
var x = 0;
var y = 0;
//used to get calculated result
var num = 0;
for (x = 1;
(x * x) < n; ++x)
{
for (y = 1; y * y < n; ++y)
{
//Calculate 4x²+y²
num = (4 * x * x) + (y * y);
if (num <= n && (num % 12 == 1 || num % 12 == 5))
{
sieve[num] = sieve[num] ^ true;
}
//Calculate 3x²+y²
num = (3 * x * x) + (y * y);
if (num <= n && num % 12 == 7)
{
sieve[num] = sieve[num] ^ true;
}
//Calculate 3x²+y²
num = (3 * x * x) - (y * y);
if (x > y && num <= n && num % 12 == 11)
{
sieve[num] = sieve[num] ^ true;
}
}
}
for (x = 5; x * x <= n; x++)
{
if (sieve[x] == true)
{
// When x is prime
// Set multiples of squares as non-prime
for (y = x * x; y <= n; y += x * x)
{
sieve[y] = false;
}
}
}
//set initial 2 prime value
if (n >= 2)
{
//set 2 is prime
sieve[2] = true;
}
if (n >= 3)
{
//set 3 is prime
sieve[3] = true;
}
process.stdout.write("\n All prime of (2 - " + n + ") is is : \n [");
//Display prime element
for (x = 0; x <= n; ++x)
{
if (sieve[x] == true)
{
process.stdout.write("  " + x);
}
}
process.stdout.write(" ]\n");
}
}

function main()
{
var obj = new SieveOfAtkin();
//Test Case
obj.sieve_of_atkin(25);
obj.sieve_of_atkin(100);
obj.sieve_of_atkin(200);
}
main();``````

#### Output

`````` All prime of (2 - 25) is is :
[  2  3  5  7  11  13  17  19  23 ]

All prime of (2 - 100) is is :
[  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 ]

All prime of (2 - 200) is is :
[  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
#  Sieve of Atkin

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

# This are used to detect prime numbers
# Set initial all the numbers are non prime
sieve = [False] * (n + 1)
#  Loop controlling variables
x = 0
y = 0
# used to get calculated result
num = 0
x = 1
while ((x * x) < n) :
y = 1
while (y * y < n) :
# Calculate 4x²+y²
num = (4 * x * x) + (y * y)
if (num <= n and(num % 12 == 1 or num % 12 == 5)) :
sieve[num] = sieve[num] ^ True

# Calculate 3x²+y²
num = (3 * x * x) + (y * y)
if (num <= n and num % 12 == 7) :
sieve[num] = sieve[num] ^ True

# Calculate 3x²+y²
num = (3 * x * x) - (y * y)
if (x > y and num <= n and num % 12 == 11) :
sieve[num] = sieve[num] ^ True

y += 1

x += 1

x = 5
while (x * x <= n) :
if (sieve[x] == True) :
#  When x is prime
#  Set multiples of squares as non-prime
y = x * x
while (y <= n) :
sieve[y] = False
y += x * x

x += 1

# set initial 2 prime value
if (n >= 2) :
# set 2 is prime
sieve[2] = True

if (n >= 3) :
# set 3 is prime
sieve[3] = True

print("\n All prime of (2 - ", n ,") is is : \n [", end = "")
# Display prime element
x = 0
while (x <= n) :
if (sieve[x] == True) :
print("  ", x, end = "")

x += 1

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

def main() :
obj = SieveOfAtkin()
# Test Case
obj.sieve_of_atkin(25)
obj.sieve_of_atkin(100)
obj.sieve_of_atkin(200)

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

#### Output

`````` All prime of (2 -  25 ) is is :
[   2   3   5   7   11   13   17   19   23 ]

All prime of (2 -  100 ) is is :
[   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 ]

All prime of (2 -  200 ) is is :
[   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
#  Sieve of Atkin

class SieveOfAtkin

# Find all prime numbers which have smaller and equal to given number n
def sieve_of_atkin(n)

if (n <= 1)

# When n are invalid to prime number
return
end
# This are used to detect prime numbers
# Set initial all the numbers are non prime
sieve = Array.new(n + 1) {false}
#  Loop controlling variables
x = 0
y = 0
# used to get calculated result
num = 0
x = 1
while ((x * x) < n)

y = 1
while (y * y < n)

# Calculate 4x²+y²
num = (4 * x * x) + (y * y)
if (num <= n && (num % 12 == 1 || num % 12 == 5))

sieve[num] = sieve[num] ^ true
end
# Calculate 3x²+y²
num = (3 * x * x) + (y * y)
if (num <= n && num % 12 == 7)

sieve[num] = sieve[num] ^ true
end
# Calculate 3x²+y²
num = (3 * x * x) - (y * y)
if (x > y && num <= n && num % 12 == 11)

sieve[num] = sieve[num] ^ true
end
y += 1
end
x += 1
end
x = 5
while (x * x <= n)

if (sieve[x] == true)

#  When x is prime
#  Set multiples of squares as non-prime
y = x * x
while (y <= n)

sieve[y] = false
y += x * x
end
end
x += 1
end
# set initial 2 prime value
if (n >= 2)

# set 2 is prime
sieve[2] = true
end
if (n >= 3)

# set 3 is prime
sieve[3] = true
end
print("\n All prime of (2 - ", n ,") is is : \n [")
# Display prime element
x = 0
while (x <= n)

if (sieve[x] == true)

print("  ", x)
end
x += 1
end
print(" ]\n")
end
end
def main()

obj = SieveOfAtkin.new()
# Test Case
obj.sieve_of_atkin(25)
obj.sieve_of_atkin(100)
obj.sieve_of_atkin(200)
end
main()``````

#### Output

`````` All prime of (2 - 25) is is :
[  2  3  5  7  11  13  17  19  23 ]

All prime of (2 - 100) is is :
[  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 ]

All prime of (2 - 200) is is :
[  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
// Sieve of Atkin

class SieveOfAtkin
{
//Find all prime numbers which have smaller and equal to given number n
def sieve_of_atkin(n: Int): Unit = {
if (n <= 1)
{
//When n are invalid to prime number
return;
}
//This are used to detect prime numbers
//Set initial all the numbers are non prime
var sieve: Array[Boolean] = Array.fill[Boolean](n + 1)(false);
// Loop controlling variables
var x: Int = 0;
var y: Int = 0;
//used to get calculated result
var num: Int = 0;
x = 1;
while ((x * x) < n)
{
y = 1;
while (y * y < n)
{
//Calculate 4x²+y²
num = (4 * x * x) + (y * y);
if (num <= n && (num % 12 == 1 || num % 12 == 5))
{
sieve(num) = sieve(num) ^ true;
}
//Calculate 3x²+y²
num = (3 * x * x) + (y * y);
if (num <= n && num % 12 == 7)
{
sieve(num) = sieve(num) ^ true;
}
//Calculate 3x²+y²
num = (3 * x * x) - (y * y);
if (x > y && num <= n && num % 12 == 11)
{
sieve(num) = sieve(num) ^ true;
}
y += 1;
}
x += 1;
}
x = 5;
while (x * x <= n)
{
if (sieve(x) == true)
{
// When x is prime
// Set multiples of squares as non-prime
y = x * x;
while (y <= n)
{
sieve(y) = false;
y += x * x;
}
}
x += 1;
}
//set initial 2 prime value
if (n >= 2)
{
//set 2 is prime
sieve(2) = true;
}
if (n >= 3)
{
//set 3 is prime
sieve(3) = true;
}
print("\n All prime of (2 - " + n + ") is is : \n [");
//Display prime element
x = 0;
while (x <= n)
{
if (sieve(x) == true)
{
print("  " + x);
}
x += 1;
}
print(" ]\n");
}
}
object Main
{
def main(args: Array[String]): Unit = {
var obj: SieveOfAtkin = new SieveOfAtkin();
//Test Case
obj.sieve_of_atkin(25);
obj.sieve_of_atkin(100);
obj.sieve_of_atkin(200);
}
}``````

#### Output

`````` All prime of (2 - 25) is is :
[  2  3  5  7  11  13  17  19  23 ]

All prime of (2 - 100) is is :
[  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 ]

All prime of (2 - 200) is is :
[  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
// Sieve of Atkin

class SieveOfAtkin
{
//Find all prime numbers which have smaller and equal to given number n
func sieve_of_atkin(_ n: Int)
{
if (n <= 1)
{
//When n are invalid to prime number
return;
}
//This are used to detect prime numbers
//Set initial all the numbers are non prime
var sieve: [Bool] = Array(repeating: false, count: n + 1);
// Loop controlling variables
var x: Int = 0;
var y: Int = 0;
//used to get calculated result
var num: Int = 0;
x = 1;
while ((x * x) < n)
{
y = 1;
while (y * y < n)
{
//Calculate 4x²+y²
num = (4 * x * x) + (y * y);
if (num <= n && (num % 12 == 1 || num % 12 == 5))
{
sieve[num] = sieve[num] != true;
}
//Calculate 3x²+y²
num = (3 * x * x) + (y * y);
if (num <= n && num % 12 == 7)
{
sieve[num] = sieve[num] != true;
}
//Calculate 3x²+y²
num = (3 * x * x) - (y * y);
if (x > y && num <= n && num % 12 == 11)
{
sieve[num] = sieve[num] != true;
}
y += 1;
}
x += 1;
}
x = 5;
while (x * x <= n)
{
if (sieve[x] == true)
{
// When x is prime
// Set multiples of squares as non-prime
y = x * x;
while (y <= n)
{
sieve[y] = false;
y += x * x;
}
}
x += 1;
}
//set initial 2 prime value
if (n >= 2)
{
//set 2 is prime
sieve[2] = true;
}
if (n >= 3)
{
//set 3 is prime
sieve[3] = true;
}
print("\n All prime of (2 - ", n ,") is is : \n [", terminator: "");
//Display prime element
x = 0;
while (x <= n)
{
if (sieve[x] == true)
{
print("  ", x, terminator: "");
}
x += 1;
}
print(" ]\n", terminator: "");
}
}
func main()
{
let obj: SieveOfAtkin = SieveOfAtkin();
//Test Case
obj.sieve_of_atkin(25);
obj.sieve_of_atkin(100);
obj.sieve_of_atkin(200);
}
main();``````

#### Output

`````` All prime of (2 -  25 ) is is :
[   2   3   5   7   11   13   17   19   23 ]

All prime of (2 -  100 ) is is :
[   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 ]

All prime of (2 -  200 ) is is :
[   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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