Math Calculators

Prime Number Checker

Check if any integer is prime, find its prime factorization, and list all divisors. Instant results for any number — runs in your browser.

Primality Test
Prime Factorization
All Divisors
Instant Results
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Integer

Enter an integer to test

Prime number checker

Prime numbers have exactly two positive divisors: one and themselves. Enter an integer to test primality and inspect prime factors.

def is_prime(n):
    return n > 1 and all(n % d for d in range(2, int(n ** 0.5) + 1))

Frequently Asked Questions

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. Examples: 2, 3, 5, 7, 11, 13…
What algorithm is used to check primality?: For numbers up to ~10 million the tool uses trial division with 6k±1 optimization. For larger numbers it uses the Miller-Rabin probabilistic primality test which is deterministic for numbers below 3.2 × 10¹⁸.
What are prime factors?: Every composite (non-prime) number can be expressed as a product of prime numbers. For example 60 = 2² × 3 × 5. This is called prime factorization.
Is 1 a prime number?: No. By definition, prime numbers must be greater than 1. The number 1 is neither prime nor composite — it is a unit.

Disclaimer

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Frequently Asked Questions

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. Examples: 2, 3, 5, 7, 11, 13…

What algorithm is used to check primality?

For numbers up to ~10 million the tool uses trial division with 6k±1 optimization. For larger numbers it uses the Miller-Rabin probabilistic primality test which is deterministic for numbers below 3.2 × 10¹⁸.

What are prime factors?

Every composite (non-prime) number can be expressed as a product of prime numbers. For example 60 = 2² × 3 × 5. This is called prime factorization.

Is 1 a prime number?

No. By definition, prime numbers must be greater than 1. The number 1 is neither prime nor composite — it is a unit.

Disclaimer

Some tools may use AI, automated processing, third-party services, or server-side processing. Do not rely on these tools as a substitute for professional advice.