Prime Number Checker
Quick answer: Enter a number to instantly see if it's prime, its prime factorization, and the nearest primes.
Enter any positive integer to check if it's prime, see its complete prime factorization (factor tree), and find the next and previous prime numbers. This calculator uses trial division — accurate for any number up to 10¹⁵.
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Last reviewed: April 2026Report an error
Prime?
✓ Prime
97 is a prime number. Next prime: 101. Previous prime: 89.
Previous Prime
89
Next Prime
101
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How to Use This Prime Checker Calculator
- 1Enter any positive integer.
- 2See immediately whether it is prime or composite.
- 3If composite, read the full prime factorization.
- 4See the next and previous prime numbers.
Frequently Asked Questions
- A prime number has exactly two distinct divisors: 1 and itself. Examples: 2, 3, 5, 7, 11, 13. The number 1 is not prime (it has only one divisor). 2 is the only even prime.
- Every composite number can be expressed as a unique product of primes. For example, 360 = 2³ × 3² × 5. This is guaranteed by the Fundamental Theorem of Arithmetic.
- Yes — Euclid proved this around 300 BCE. His proof: assume a finite list of primes, multiply them all and add 1 — the result is either prime or has a prime factor not in the list. Contradiction.
- As of 2024, the largest known prime is 2^136,279,841 − 1, a Mersenne prime with over 41 million digits, discovered by the Great Internet Mersenne Prime Search (GIMPS).
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