Prime Number Checker

Using the prime checker is straightforward:

Enter your number. Type or paste any positive integer into the input field. The checker supports numbers up to 15 digits.

Get instant results. The tool immediately tells you whether the number is prime or composite. For composite numbers, it also lists all factors.

Explore nearby primes. The tool shows the nearest prime above and below your number, making it easy to explore the distribution of primes.

• Real-time checking — results appear as you type
• Factor breakdown — see all divisors for composite numbers
• Nearest primes — quickly find the closest primes
• Large number support — handles numbers up to quadrillions

The simplest way to check if a number n is prime is trial division: test whether any integer from 2 to √n divides it evenly. If none do, the number is prime.

For larger numbers, this tool uses the Miller-Rabin primality test, a probabilistic algorithm that is extremely fast and deterministic for numbers below 3.3 × 10¹⁴ when using specific witness values.

Key concepts:

• 1 is not prime — by mathematical convention, 1 is neither prime nor composite
• 2 is the only even prime — all other even numbers are divisible by 2
• There are infinitely many primes — proven by Euclid around 300 BCE
• Prime gaps grow — the distance between consecutive primes generally increases, but twin primes (like 11 and 13) appear throughout

Prime numbers are foundational to many fields:

• Cryptography: RSA encryption relies on the difficulty of factoring products of two large primes. Every secure HTTPS connection uses prime-based math.
• Computer science: Hash tables often use prime-sized arrays to minimize collisions. Pseudorandom number generators use prime moduli.
• Mathematics: The distribution of primes is connected to the Riemann Hypothesis, one of the most famous unsolved problems in math.
• Competitive programming: Primality testing and prime factorization are among the most common algorithmic challenges in contests like Codeforces and LeetCode.