Prime Number Checker

Step 1: Enter any positive whole number up to one trillion.

Step 2: Click Calculate.

Step 3: See whether the number is prime. If composite, the result includes the full prime factorization.

A prime number is a whole number greater than 1 whose only positive divisors are 1 and itself. In other words, you cannot divide a prime number by any smaller whole number (except 1) without leaving a remainder.

The first ten prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. The number 2 is the only even prime — every other even number is divisible by 2.

Numbers that are not prime (and not 1) are called 'composite.' Every composite number can be written uniquely as a product of primes — this is the fundamental theorem of arithmetic, and it underpins number theory, cryptography, and modern computer security.

Trial division method:
1. If n < 2 → not prime
2. If n = 2 → prime
3. If n is even → not prime
4. Check odd divisors from 3 up to √n. If any divide n evenly, n is composite.
5. If no divisor is found → prime.

Why only up to √n? If n has a factor larger than √n, its paired factor must be smaller than √n — so you would have found it already.

Example: Is 29 prime? √29 ≈ 5.39. Check 3, 5. Neither divides 29 → prime.

Example 1: 17 → Prime. Tested 3 (17/3 ≈ 5.67, not whole). √17 ≈ 4.12, so no more checks needed.

Example 2: 91 → Not prime. 91 = 7 × 13. A common trick question — looks prime but isn't.

Example 3: 1 → Not prime. By definition, primes must be greater than 1.

1 is not prime — by modern definition, primes must be greater than 1.

2 is the only even prime. All other even numbers are composite.

91 is not prime — a classic trick (91 = 7 × 13).

RSA encryption relies on the difficulty of factoring large primes.