Check Prime Numbers and Find Factors

Instantly determine if any number is prime. If it’s composite, this tool provides the full prime factorization—no manual division required.

Why Use This Tool?

• Simplify Math: Quickly verify fraction reductions or solve complex number theory problems.
• Master Cryptography: Explore the mathematical building blocks of the encryption algorithms that secure the internet.
• Find "Prime Days": See if your birthday, anniversary, or lucky number is prime.

Key Features

• Instant Factorization: If a number isn't prime, the tool breaks it down into its prime components (e.g., 12 → 2 × 2 × 3).
• Locate Neighbors: Discover the nearest prime numbers immediately preceding and following your input.
• Generate Prime Lists: Use the Range Generator to list every prime number up to 100,000 for study or data projects.

FAQ

What is the maximum number I can check? You can test integers up to approximately 9 quadrillion (Number.MAX_SAFE_INTEGER). Beyond this limit, standard computing methods lose the precision necessary for a guaranteed result.

Why aren't 0 and 1 considered prime? Mathematically, a prime number must have exactly two distinct divisors: 1 and itself. Because 1 only has one divisor and 0 has infinitely many, neither fits the definition.

How fast is the calculation? Tests are near-instant. The tool uses optimized primality algorithms to ensure you get results in milliseconds, even for large numbers.

Trivia: The Atoms of Mathematics

Primes are the "Atoms of Mathematics" because every whole number greater than 1 is either a prime or a unique product of primes. This concept is the backbone of modern cybersecurity. RSA encryption, which secures your online transactions, relies on a mathematical asymmetry: it is easy to multiply two massive primes, but incredibly difficult for even the world’s most powerful supercomputers to factor the result back into the original primes.