Java program to check if a number is prime or not
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.
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 "); } } |
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)
Example : Check number is prime or not using function.
Java
/*package whatever //do not write package name here */ import java.io.*; import java.util.Scanner; class Program { /*function to check prime or not*/ static void prime( int no) { int count = 0 ; for ( int i = 1 ; i <= no; i++) { if (no % i == 0 ) count++; } if (count == 2 ) System.out.println(no + " is prime" ); else System.out.println(no + " is not prime" ); } public static void main(String[] args) { prime( 13 ); // calling prime( 20 ); prime( 23 ); } } |
Output
13 is prime 20 is not prime 23 is prime
Please Login to comment...