Prime Number Checker & Factorization Tool
Test whether any integer is a prime or composite number using deterministic trial division and Miller-Rabin primality tests. View complete prime factor decompositions, all integer divisors, and nearby prime numbers.
How to Use Prime Number Checker & Factorizer
Enter Any Integer
Input any positive integer up to 15 digits.
Check Primality
View instant verdict: PRIME or COMPOSITE.
Inspect Factors
Examine the prime factor tree, exponent decomposition, and full list of divisors.
About Prime Number Checker & Factorizer
A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers (it has exactly two positive divisors: 1 and itself). By the Fundamental Theorem of Arithmetic, every integer greater than 1 has a unique prime factorization.
Key Features
- Ultra-fast primality testing algorithm (trial division up to √n + Miller-Rabin test)
- Complete Prime Factorization with canonical exponent notation (e.g. 360 = 2³ × 3² × 5)
- Total count and complete list of all positive divisors
- Identifies the previous prime and next upcoming prime number
- Fun mathematical facts (Twin primes, Mersenne primes, Sophie Germain primes)
Frequently Asked Questions
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