Prime Number Checker
Check if a number is prime instantly. Find prime factors, nearest primes, and the nth prime number online.
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, 17, 19...
How does the prime checker work?
The tool uses efficient algorithms to test divisibility. It checks if the number can be divided evenly by any integer up to its square root, which is mathematically sufficient to determine primality.
What is prime factorization?
Prime factorization is expressing a number as a product of prime numbers. For example, 12 = 2 × 2 × 3, and 36 = 2 × 2 × 3 × 3.
Is 1 a prime number?
No, 1 is not considered a prime number. By definition, prime numbers must be greater than 1. The smallest prime number is 2.
Why is 2 the only even prime number?
All other even numbers are divisible by 2, so they have at least three divisors: 1, 2, and themselves. Only 2 has exactly two divisors: 1 and 2.
What are the nearest primes?
Nearest primes are the closest prime numbers before and after a given number. For example, the nearest primes to 10 are 7 (before) and 11 (after).
What is the nth prime number?
The nth prime is the prime number at position n in the sequence of primes. For example, the 1st prime is 2, the 5th prime is 11, and the 100th prime is 541.
Is my data sent to a server?
No, all calculations are done entirely in your browser using JavaScript. Your numbers are never transmitted to any server, ensuring complete privacy.
How large a number can I check?
The tool can handle very large numbers efficiently. For extremely large numbers (millions of digits), performance may vary depending on your device's capabilities.
What are prime numbers used for?
Prime numbers are fundamental in cryptography (RSA encryption), hash functions, random number generators, and various mathematical proofs. They're also used in computer science algorithms.
Can I check negative numbers or decimals?
Prime numbers are defined only for natural numbers greater than 1. Negative numbers, zero, fractions, and decimals cannot be prime.
Is there a formula to find all prime numbers?
No simple formula exists that generates all prime numbers. However, various algorithms and tests (like the Sieve of Eratosthenes) can efficiently find primes within a range.
How to Use Prime Number Checker
Check whether any number is prime, factor it, and explore nearby primes without leaving your browser. Every test runs locally, and nothing you type is uploaded.
- Type an integer into the Number field — the Enter a number (e.g. 17) placeholder shows the expected format.
- Read the primality verdict that appears immediately as you finish typing.
- Tick Show prime factors to break a composite number into its prime building blocks.
- Tick Show divisors to list every integer that divides your number with no remainder.
- Tick Find nearest primes to reveal the closest prime below and above your value.
For very large numbers JavaScript loses exact integer precision; stay below 2^53 − 1 (about 9×10^15) to keep results exact.
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