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Check whether any number is prime — and find the prime factorisation of non-prime numbers. Supports large numbers.
Prime Number Checker · divisor list and factorization · 100% private client-side
Type any positive integer. The result updates instantly for small numbers.
Prime (with confirmation it has exactly two factors: 1 and itself) or composite (with the full prime factorisation).
Optionally generate all primes up to a specified limit using the Sieve of Eratosthenes.
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The first prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29… 2 is the only even prime number; all other even numbers are divisible by 2 and therefore not prime.
Every composite (non-prime) integer greater than 1 can be expressed as a unique product of prime numbers — this is the Fundamental Theorem of Arithmetic. Example: 360 = 2³ × 3² × 5. Prime factorisation is used in GCD/LCM calculations, cryptography, and number theory.
The checker handles numbers up to approximately 10^15 using optimised trial division with early termination. For very large numbers (cryptographically large primes), probabilistic primality tests like Miller-Rabin would be needed — this tool uses deterministic checks within the supported range.
No. 1 is not considered prime. By definition, prime numbers must have exactly two distinct divisors (1 and themselves) — the number 1 has only one divisor (itself). This exclusion is important for the Fundamental Theorem of Arithmetic to hold uniquely.
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Prime numbers are the building blocks of arithmetic — every integer factors into primes uniquely — and primality testing is a fundamental concept in both pure mathematics and applied cryptography (RSA encryption depends entirely on the computational difficulty of factoring large semiprimes). This checker handles numbers up to 10^15 with a fast deterministic algorithm and shows the full prime factorisation for composite numbers, making it useful for number theory homework, programming exercises, and verifying factorisation results. The Sieve of Eratosthenes feature generates all primes up to a user-specified limit — useful for generating prime lists for competitive programming and mathematical exploration.
All calculations run in your browser. No data is transmitted to any server.
