Prime Number Calculator

Explore the Building Blocks of Numbers

A prime number is a whole number greater than 1 that has no positive divisors other than 1 and itself. This tool helps you explore the world of prime numbers in two ways: by testing if a specific number is prime, and by generating a list of all primes up to a certain limit.

The Calculation Explained

• Primality Test: The calculator uses a method called trial division. It checks if the input number is divisible by any integer from 2 up to its square root. If no divisors are found, the number is prime.
• Prime Generation: The calculator iterates through all numbers up to the specified limit and performs a primality test on each one, listing those that are prime.

How to Use the Calculator

• To Check a Number: Enter a number in the first input field and click 'Check Primality'.
• To Generate Primes: Enter an upper limit in the second input field and click 'Generate Primes Up To'.

Real-World Example

• You want to check if 29 is a prime number.
  • The calculator checks for divisibility by 2, 3, 4, and 5. Since √29 is about 5.4, it doesn't need to check further. No divisors are found, so the calculator reports that 29 is a prime number.
• You want to generate all primes up to 20.
  • The calculator will test each number and return the list: 2, 3, 5, 7, 11, 13, 17, 19.

Frequently Asked Questions (FAQ)

• Is 1 a prime number? No. By definition, a prime number must be greater than 1.
• Is 2 a prime number? Yes. It is the only even prime number.
• Why are prime numbers important? Prime numbers are the fundamental building blocks of all whole numbers (Fundamental Theorem of Arithmetic). They are also critically important in modern cryptography, which secures almost all digital communication.