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Q: Write a Java program that checks if a given number is a prime number. A prime number is a number greater than 1 that has no divisors other than 1 and itself. Your program should take an integer as input and output whether it is a prime number or not.
Prime Number
Employee Hierarchy:
class prime
{
public static void main(String arg[])
{
int i,m=0,flag=0;
int n=4;
m=n/2;
if(n==0||n==1)
{
System.out.print(n+" is not prime num");
}
else
{
for(i=2;i<=m;i++)
if(n%i==0)
{
System.out.print(n+" is not prime num");
flag=1;
break;
}
}
if(flag==0){
System.out.print(n+" is prime num");
}
}
}
Out Put
prime number by scanner
import java.util.Scanner;
public class PrimeNumberChecker {
public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);
System.out.print("Enter a number to check if it's prime: ");
int number = scanner.nextInt();
if (isPrime(number)) {
System.out.println(number + " is a prime number.");
} else {
System.out.println(number + " is not a prime number.");
}
}
// Function to check if a number is prime
public static boolean isPrime(int n) {
if (n <= 1) {
return false;
}
// Check from 2 to square root of n
for (int i = 2; i <= Math.sqrt(n); i++) {
if (n % i == 0) {
return false;
}
}
return true;
}
}
Prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves. In other words, a prime number is a number that is divisible only by 1 and itself.
For example, 2, 3, 5, 7, 11, 13, 17, 19, and so on, are prime numbers because they cannot be divided evenly by any other number except 1 and themselves.
Here are some key points about prime numbers:
1. **Divisibility**: A prime number is only divisible by 1 and itself. If a number has divisors other than 1 and itself, it is called a composite number.
2. **Unique Factorization**: Every positive integer greater than 1 can be represented uniquely as a product of prime numbers. This is known as the Fundamental Theorem of Arithmetic. For example, 12 can be expressed as \(2^2 \times 3\), where 2 and 3 are prime numbers. This representation is unique.
3. **Density**: Prime numbers become less frequent as you move along the number line. However, there are infinitely many prime numbers. This was proved by Euclid around 300 BCE.
4. **Applications**: Prime numbers have significant applications in various fields such as cryptography, number theory, and computer science. They are used in algorithms for encryption, hashing, and generating random numbers.
5. **Prime Factorization**: Finding the prime factors of a number is a fundamental operation in number theory. It involves decomposing a number into its prime factors.
6. **Sieve of Eratosthenes**: It’s an ancient algorithm used to find all prime numbers up to a given limit. It works by iteratively marking the multiples of each prime number starting from 2 as composite.
Prime numbers are fascinating objects in mathematics and have been studied for centuries, with many open questions still remaining about their distribution and properties.
