Given a positive integer, check if the number is prime or not. A prime is a natural number greater than 1 that has no positive divisors other than 1 and itself. Examples of first few prime numbers are {2, 3, 5,
Examples :
Input: n = 11 Output: true Input: n = 15 Output: false Input: n = 1 Output: false
School Method
A simple solution is to iterate through all numbers from 2 to n-1 and for every number check if it divides n. If we find any number that divides, we return false.
Below is the implementation of this method.
C++
// A school method based C++ program to check if a
// number is prime
#include <bits/stdc++.h>
using namespace std;
bool isPrime(int n)
{
// Corner case
if (n <= 1) return false;
// Check from 2 to n-1
for (int i=2; i<n; i++)
if (n%i == 0)
return false;
return true;
}
// Driver Program to test above function
int main()
{
isPrime(11)? cout << " true\n": cout << " false\n";
isPrime(15)? cout << " true\n": cout << " false\n";
return 0;
}
Java
// A school method based JAVA program
// to check if a number is prime
class GFG {
static boolean isPrime(int n)
{
// Corner case
if (n <= 1) return false;
// Check from 2 to n-1
for (int i = 2; i < n; i++)
if (n % i == 0)
return false;
return true;
}
// Driver Program
public static void main(String args[])
{
if(isPrime(11))
System.out.println(" true");
else
System.out.println(" false");
if(isPrime(15))
System.out.println(" true");
else
System.out.println(" false");
}
}
// This code is contributed
// by Nikita Tiwari.
Python3
# A school method based Python3
# program to check if a number
# is prime
def isPrime(n):
# Corner case
if n <= 1:
return False
# Check from 2 to n-1
for i in range(2, n):
if n % i == 0:
return False;
return True
# Driver Program to test above function
print("true") if isPrime(11) else print("false")
print("true") if isPrime(14) else print("false")
# This code is contributed by Smitha Dinesh Semwal
C#
// A optimized school method based C#
// program to check if a number is prime
using System;
namespace prime
{
public class GFG
{
public static bool isprime(int n)
{
// Corner cases
if (n <= 1) return false;
for (int i = 2; i < n; i++)
if (n % i == 0)
return false;
return true;
}
// Driver program
public static void Main()
{
if (isprime(11)) Console.WriteLine("true");
else Console.WriteLine("false");
if (isprime(15)) Console.WriteLine("true");
else Console.WriteLine("false");
}
}
}
// This code is contributed by Sam007
PHP
<?php
// A school method based PHP
// program to check if a number
// is prime
function isPrime($n)
{
// Corner case
if ($n <= 1) return false;
// Check from 2 to n-1
for ($i = 2; $i < $n; $i++)
if ($n % $i == 0)
return false;
return true;
}
// Driver Code
$tet = isPrime(11) ? " true\n" :
" false\n";
echo $tet;
$tet = isPrime(15) ? " true\n" :
" false\n";
echo $tet;
// This code is contributed by m_kit
?>
Output :
true false
Time complexity of this solution is O(n)
Optimized School Method
We can do following optimizations:
- Instead of checking till n, we can check till √n because a larger factor of n must be a multiple of smaller factor that has been already checked.
- The algorithm can be improved further by observing that all primes are of the form 6k ± 1, with the exception of 2 and 3. This is because all integers can be expressed as (6k + i) for some integer k and for i = ?1, 0, 1, 2, 3, or 4; 2 divides (6k + 0), (6k + 2), (6k + 4); and 3 divides (6k + 3). So a more efficient method is to test if n is divisible by 2 or 3, then to check through all the numbers of form 6k ± 1. (Source: wikipedia)
- Primality Test | Set 2 (Fermat Method)
- Sieve of Eratosthenes
- Primality Test | Set 3 (Miller–Rabin)
- Efficient program to print all prime factors of a given number
- Prime Numbers
- Find (a^b)%m where ‘b’ is very large
- Minimum operations required to make all the elements distinct in an array
- Check if a M-th fibonacci number divides N-th fibonacci number
- Number of triangles in a plane if no more than two points are collinear
- Sum of digits equal to a given number in PL/SQL
Below is the implementation of this solution.
C++
// A optimized school method based C++ program to check
// if a number is prime
#include <bits/stdc++.h>
using namespace std;
bool isPrime(int n)
{
// Corner cases
if (n <= 1) return false;
if (n <= 3) return true;
// This is checked so that we can skip
// middle five numbers in below loop
if (n%2 == 0 || n%3 == 0) return false;
for (int i=5; i*i<=n; i=i+6)
if (n%i == 0 || n%(i+2) == 0)
return false;
return true;
}
// Driver Program to test above function
int main()
{
isPrime(11)? cout << " true\n": cout << " false\n";
isPrime(15)? cout << " true\n": cout << " false\n";
return 0;
}
Java
// A optimized school method based Java
// program to check if a number is prime
import java.io.*;
class GFG {
static boolean isPrime(int n)
{
// Corner cases
if (n <= 1) return false;
if (n <= 3) return true;
// This is checked so that we can skip
// middle five numbers in below loop
if (n % 2 == 0 || n % 3 == 0) return false;
for (int i = 5; i * i <= n; i = i + 6)
if (n % i == 0 || n % (i + 2) == 0)
return false;
return true;
}
// Driver Program
public static void main(String args[])
{
if(isPrime(11))
System.out.println(" true");
else
System.out.println(" false");
if(isPrime(15))
System.out.println(" true");
else
System.out.println(" false");
}
}
/*This code is contributed by Nikita Tiwari.*/
Python3
# A optimized school method based
# Python3 program to check
# if a number is prime
def isPrime(n) :
# Corner cases
if (n <= 1) :
return False
if (n <= 3) :
return True
# This is checked so that we can skip
# middle five numbers in below loop
if (n % 2 == 0 or n % 3 == 0) :
return False
i = 5
while(i * i <= n) :
if (n % i == 0 or n % (i + 2) == 0) :
return False
i = i + 6
return True
# Driver Program
if(isPrime(11)) :
print(" true")
else :
print(" false")
if(isPrime(15)) :
print(" true")
else :
print(" false")
# This code is contributed
# by Nikita Tiwari.
C#
// A optimized school method based C#
// program to check if a number is prime
using System;
class GFG
{
public static bool isPrime(int n)
{
// Corner cases
if (n <= 1) return false;
if (n <= 3) return true;
// This is checked so that we
// can skip middle five numbers
// in below loop
if (n % 2 == 0 || n % 3 == 0) return false;
for (int i = 5; i * i <= n; i = i + 6)
if (n % i == 0 || n % (i + 2) == 0)
return false;
return true;
}
// Driver Code
public static void Main()
{
if (isPrime(11)) Console.WriteLine("true");
else Console.WriteLine("false");
if (isPrime(15)) Console.WriteLine("true");
else Console.WriteLine("false");
}
}
// This code is contributed by aj_36
PHP
<?php
// A optimized school method
// based PHP program to check
// if a number is prime
function isPrime($n)
{
// Corner cases
if ($n <= 1)
return false;
if ($n <= 3)
return true;
// This is checked so that we can skip
// middle five numbers in below loop
if ($n % 2 == 0 || $n % 3 == 0)
return false;
for($i = 5; $i * $i <= $n; $i = $i + 6)
if ($n % $i == 0 || $n % ($i + 2) == 0)
return false;
return true;
}
// Driver Code
if(isPrime(11))
echo " true\n";
else
echo " false\n";
if(isPrime(15))
echo " true\n";
else
echo " false\n";
// This code is contributed ajit
?>
Output :
true false
Time complexity of this solution is O(√n)
Primality Test | Set 2 (Fermat Method)
References:
https://en.wikipedia.org/wiki/Prime_number
http://www.cse.iitk.ac.in/users/manindra/presentations/FLTBasedTests.pdf
https://en.wikipedia.org/wiki/Primality_test
This article is contributed by Ajay. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
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