How large a number can I check?

Up to 10¹² (one trillion). The Miller-Rabin test used here is deterministic for numbers up to 3.3 × 10²⁴ using the first 13 prime witnesses.

What is a Mersenne prime?

A Mersenne prime is a prime of the form 2ⁿ − 1. Examples: 3 (2²−1), 7 (2³−1), 31 (2⁵−1), 127 (2⁷−1). They are named after French monk Marin Mersenne.

What is a twin prime?

Twin primes are pairs of primes that differ by 2. Examples: (3,5), (11,13), (17,19). The twin prime conjecture says there are infinitely many such pairs, though it remains unproven.

What is a safe prime?

A prime p is safe if (p−1)/2 is also prime. Safe primes are used in cryptography (e.g., Diffie-Hellman). Examples: 5, 7, 11, 23, 47.

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Prime Number Checker

Check if any number up to 10¹² is prime, see its factorization, and explore related prime facts.

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About this tool

Enter any integer up to one trillion and find out instantly whether it is prime. Uses the Miller-Rabin primality test for large numbers. Shows prime factorization for composite numbers, finds the next and previous primes, identifies special primes (Mersenne, twin, safe), and can generate the first N primes.

How to use

1 Enter a positive integer into the number field.
2 Click Check to test primality and see factorization.
3 Use Next Prime and Prev Prime to navigate the prime sequence.
4 Set a count and click Generate Primes to list the first N primes.

Frequently Asked Questions

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