How to Use the Calculator
- Enter a positive integer greater than or equal to 2 in the input field.
- Click the "Calculate" button to check if the number is prime.
- The calculator will display whether the number is prime and provide additional details if it is.
Understanding Prime Numbers
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, 7, 11, and 13 are prime numbers.
Calculation Method
The calculator uses the following method to determine if a number is prime:
- It first checks if the number is less than or equal to 1 (not prime).
- It then checks if the number is 2 or 3 (prime).
- For numbers greater than 3, it checks divisibility by 2 and 3.
- The algorithm then checks for divisibility by all integers of the form 6k ± 1 up to the square root of the number.
- If no divisors are found, the number is prime.
Additional Information
When the calculator identifies a prime number, it also provides:
- The prime factors of the number (if it were not prime)
- An estimate of the position of the number in the sequence of all prime numbers
Examples
- Example 1: Enter 17. The calculator will show that 17 is prime.
- Example 2: Enter 18. The calculator will show that 18 is not prime and display its prime factors: 2, 3, 3.