Math Tools
Prime Number Checker
Check if a number is prime instantly. Test primality, find prime factorization, list all prime numbers up to N, and learn about prime properties. Works with numbers up to 10 million.
Use Prime Number Checker to get instant results without uploads or sign-ups. Everything runs securely in your browser for fast, reliable output.
Your results will appear here.
About this tool
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In other words, a prime number can only be divided evenly by 1 and itself. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29... Prime numbers are the building blocks of mathematics - every positive integer can be expressed as a unique product of prime numbers (Fundamental Theorem of Arithmetic).
Our Prime Number Checker uses an optimized algorithm to test primality instantly. For small numbers, it uses trial division (checking divisibility up to √n). For larger numbers, it employs more sophisticated primality tests. The tool not only tells you if a number is prime but also provides prime factorization for composite numbers, showing you the unique prime factors that multiply to give your number.
Prime numbers have fascinated mathematicians for thousands of years and have important applications in modern technology. They are crucial for: cryptography and internet security (RSA encryption uses very large primes), hash tables and hash functions, random number generation, and various algorithms in computer science. Finding very large prime numbers remains an active area of research and computation.
Understanding prime numbers helps with: factoring numbers, finding GCD and LCM, simplifying fractions, solving number theory problems, and appreciating the beauty of mathematics. Interesting facts: 2 is the only even prime number (all other even numbers are divisible by 2). There are infinitely many prime numbers (proven by Euclid around 300 BC). The largest known prime number (as of 2024) has over 24 million digits!
Usage examples
Small Prime Number
Check if 17 is prime
Input: 17. Result: ✅ PRIME - 17 is a prime number. Next prime: 19. Previous prime: 13. 17 is the 7th prime number.
Composite Number
Check if 24 is prime
Input: 24. Result: ❌ COMPOSITE - 24 is not prime. Prime Factorization: 2³ × 3 = 2 × 2 × 2 × 3. Divisors: 1, 2, 3, 4, 6, 8, 12, 24.
Large Prime
Check if 104729 is prime
Input: 104729. Result: ✅ PRIME - 104729 is a prime number. This is the 10,000th prime number.
Power of 2
Check if 128 is prime
Input: 128. Result: ❌ COMPOSITE - 128 = 2⁷. Perfect power of 2. Prime Factorization: 2⁷.
Famous Prime
Check Mersenne prime 8191
Input: 8191. Result: ✅ PRIME - 8191 is a Mersenne prime (2¹³ - 1). These primes have form 2ᵖ - 1 where p is prime.
How to use
- Enter any positive integer in the input field (up to 10 million)
- Click "Check Prime" to instantly test if the number is prime
- View whether the number is prime or composite
- See prime factorization for composite numbers
- Get the list of all prime factors and nearest primes
- Learn interesting mathematical properties about the number
Benefits
- Instant primality testing for any number up to 10 million
- Prime factorization for composite numbers
- Shows all divisors and factors
- Finds nearest prime numbers (next and previous)
- Counts prime factors with exponents (e.g., 2³ × 3)
- Educational: explains WHY a number is or isn't prime
- Identifies special types: Mersenne primes, perfect squares, powers
- Shows position in prime number sequence
- Useful for homework, cryptography, number theory
- Works offline, completely private
- Free forever, no registration
- Mobile-friendly interface
FAQs
What makes a number prime?
A prime number must be: (1) a natural number greater than 1, (2) divisible only by 1 and itself with no remainder. For example, 7 is prime because only 1 × 7 = 7. But 6 is not prime because 1 × 6 = 6 AND 2 × 3 = 6 (it has other divisors). Numbers with more than two divisors are called composite numbers. Special case: 1 is neither prime nor composite by definition.
Is 1 a prime number?
No, 1 is NOT a prime number by mathematical convention. This definition is important for the Fundamental Theorem of Arithmetic to work (unique prime factorization). If 1 were prime, then 6 = 2 × 3 = 1 × 2 × 3 = 1 × 1 × 2 × 3... would have infinitely many factorizations. By excluding 1, every number has exactly one prime factorization.
Is 2 a prime number?
Yes! 2 is prime AND it's the ONLY even prime number. 2 is divisible only by 1 and 2, meeting the definition perfectly. All other even numbers (4, 6, 8, 10...) are divisible by 2, making them composite. This makes 2 special - it's often called "the oddest prime" because it's the only even one.
How do you check if a large number is prime?
For small numbers, test division by all numbers from 2 to √n (since any factor larger than √n must pair with one smaller). For example, to check if 97 is prime, test division by 2, 3, 5, 7 (up to √97 ≈ 9.8). None divide evenly, so 97 is prime. For huge numbers (100+ digits), use advanced tests like Miller-Rabin or AKS primality test. Our calculator handles numbers up to 10 million efficiently.
What is prime factorization?
Prime factorization breaks a number into prime numbers that multiply to give the original. Example: 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5. This is unique for every number (Fundamental Theorem). It's useful for: finding GCD and LCM, simplifying fractions, cryptography, and understanding number structure. To factor: divide by smallest primes (2, 3, 5...) until you reach 1.
How many prime numbers are there?
There are infinitely many prime numbers (proven by Euclid around 300 BC using proof by contradiction). However, they become increasingly rare as numbers get larger. Up to 100 there are 25 primes. Up to 1,000 there are 168 primes. Up to 1,000,000 there are 78,498 primes. The density decreases approximately as 1/ln(n) by the Prime Number Theorem.
What are twin primes?
Twin primes are pairs of prime numbers that differ by 2, like (3,5), (5,7), (11,13), (17,19), (29,31), (41,43). The Twin Prime Conjecture says there are infinitely many twin primes, but this hasn't been proven yet (one of mathematics' unsolved problems). Largest known twin primes have over 200,000 digits each!
Why are prime numbers important in cryptography?
RSA encryption (used for HTTPS, digital signatures, secure messaging) relies on the difficulty of factoring very large numbers into primes. It's easy to multiply two 100-digit primes to get a 200-digit number, but extremely hard to factor that 200-digit number back to find the original primes. This asymmetry creates secure encryption - your public key uses the product, your private key uses the factors. Breaking it requires factoring a huge number, which is computationally infeasible.
Related tools
View all toolsFibonacci Calculator
Calculate Fibonacci sequence numbers, find the Nth Fibonacci number, generate sequences, and explore the golden ratio. Perfect for mathematics, nature patterns, and programming.
Math ToolsFraction Calculator
Calculate fractions: add, subtract, multiply, divide. Simplify fractions, convert to decimals, and find common denominators.
Math ToolsGolden Ratio Calculator
Calculate golden ratio (φ = 1.618) proportions for design, art, and architecture. Find harmonious dimensions using the divine proportion.
Math Tools