Problem Statement

Write a Java program to check if a given number is a prime number. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. For example, 2, 3, 5, and 7 are prime numbers, whereas 4, 6, 8, and 9 are not.

Examples

Example 1:

• Input: 7
• Output: 7 is a prime number.
• Justification: The number 7 has no divisors other than 1 and 7, making it a prime number.

Example 2:

• Input: 10
• Output: 10 is not a prime number.
• Justification: The number 10 can be divided evenly by 1, 2, 5, and 10, indicating that it is not a prime number.

Step-by-Step Algorithm

To determine whether a number is prime, follow these steps:

1. Initialize the Number:

   • Let num be the number to check for primality.

2. Handle Special Cases:

   • If num is less than or equal to 1, it is not a prime number.
   • If num is 2, it is a prime number (the only even prime).

3. Check for Even Numbers:

   • If num is even and greater than 2, it is not a prime number.

4. Check for Divisors:

   • Iterate from 3 to the square root of num, incrementing by 2 (since even numbers have already been handled).
   • For each iteration, check if num is divisible by the current iterator value.
   • If a divisor is found, num is not a prime number.

5. Conclusion:

   • If no divisors are found in the above steps, num is a prime number.

Code

Below is the Java code that demonstrates how to check if a number is prime using the described algorithm. This example checks whether the number 7 is prime.