Prime Number Checker Check if a number is prime and find its factors and nearest primes.
Prime Number Checker
Check if a number is prime and find its factors and nearest primes.
Enter a Number
Type any positive integer to check whether it is prime.
See the Result
The tool instantly tells you if the number is prime or not.
Explore Factors
For non-prime numbers, view all factors and the nearest prime numbers.
What Is Prime Number Checker?
A prime number checker determines whether a given integer is a prime number — a natural number greater than 1 that has no positive divisors other than 1 and itself. The first few primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. Note that 2 is the only even prime number. If a number is not prime (composite), the checker also lists all its factors and identifies the nearest prime numbers both above and below. Prime numbers are the fundamental building blocks of all integers (every integer > 1 can be uniquely expressed as a product of primes), making them essential in number theory, cryptography (RSA encryption relies on the difficulty of factoring large numbers), hash functions, and random number generation. This tool uses an optimized trial division algorithm that only tests divisors up to the square root of the input, making it efficient even for large numbers up to one trillion.
Why Use Prime Number Checker?
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Instantly tests primality for numbers up to 1 trillion
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Lists all factors for non-prime numbers
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Shows nearest prime numbers above and below
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Uses optimized trial division algorithm
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Clear visual indicator for prime/not-prime results
Common Use Cases
Mathematics Education
Learn about prime numbers and verify primality for homework problems.
Cryptography
Find prime numbers for RSA key generation and other cryptographic applications.
Number Theory Research
Explore properties of prime numbers and their distribution.
Programming Challenges
Verify solutions to prime-related coding challenges and algorithms.
Technical Guide
The primality test uses optimized trial division. First, numbers less than 2 are immediately classified as not prime. Numbers 2 and 3 are prime. Then we check divisibility by 2 and 3. For remaining candidates, we test divisors of the form 6k±1 (i.e., 5, 7, 11, 13, 17, 19, ...) up to √n. This works because all primes greater than 3 are of the form 6k±1 (numbers of the form 6k, 6k+2, 6k+3, 6k+4 are divisible by 2 or 3). This optimization reduces the number of trial divisions by a factor of 3 compared to naive trial division. For the factor-finding function, we iterate from 1 to √n, collecting both i and n/i whenever n%i === 0. The nearest-prime search iterates outward from n, testing each integer for primality until a prime is found in each direction.
Tips & Best Practices
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12 is the only even prime number — all other even numbers are divisible by 2
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2To check primality by hand, you only need to test divisors up to √n
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3All primes greater than 3 are of the form 6k ± 1
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4The number 1 is neither prime nor composite by mathematical convention
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5There are infinitely many prime numbers (proven by Euclid around 300 BC)
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🔢 Math & CalculatorsFrequently Asked Questions
Q Is 1 a prime number?
Q Is 2 a prime number?
Q How large a number can I check?
Q Why are prime numbers important in cryptography?
Q What is the largest known prime?
About This Tool
Prime Number Checker is a free online tool by FreeToolkit.ai. All processing happens directly in your browser — your data never leaves your device. No registration or installation required.