Prime Number Checker
Check if any number is prime and list its prime factors instantly. Also generates a list of prime numbers up to any limit.
🧮 Math & Finance Tools
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List Primes up to…
What is a Prime Number?
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The first primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29… There are infinitely many primes — Euclid proved this around 300 BCE.
Special Cases
| Number | Classification |
|---|---|
| 0, 1 | Neither prime nor composite by definition |
| 2 | The only even prime |
| Primes | Exactly 2 divisors: 1 and itself |
| Composites | More than 2 divisors; product of primes |
Why Primes Matter
Prime numbers are the foundation of modern cryptography. RSA encryption — used in HTTPS, banking and secure messaging — relies on the computational difficulty of factoring the product of two large primes. The Fundamental Theorem of Arithmetic states every integer > 1 is uniquely expressible as a product of primes.