Prime Number Checker

Instantly verify if any number is prime with our free, real-time tool. Handles numbers up to 10100 efficiently.

Check a Number

Enter a positive integer greater than 1

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Result

Enter a number and click "Check Prime Status"

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. This means prime numbers can only be divided evenly by 1 and the number itself.

The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and so on. Prime numbers play a fundamental role in mathematics, especially in number theory, and have practical applications in cryptography, computer science, and cybersecurity.

Why Use Our Prime Number Checker?

  • Real-time processing with instant results
  • Handles numbers up to 10100 efficiently
  • 100% free with no signup required
  • Educational tool for students and teachers

How Prime Numbers Are Used

Prime numbers are essential in modern cryptography. Algorithms like RSA encryption rely on the difficulty of factoring large prime numbers to secure online communications, e-commerce transactions, and digital signatures. Prime numbers also have applications in hash functions, random number generation, and error detection.

Advanced Algorithm

Our tool uses an optimized algorithm that handles large numbers efficiently:

  • For numbers ≤ 1012: Deterministic trial division
  • For numbers > 1012: Miller-Rabin probabilistic test with 5 iterations
  • For numbers > 1050: Miller-Rabin with 10 iterations for higher accuracy
  • Special handling for even numbers and multiples of small primes

Frequently Asked Questions

What is the largest known prime number?

How does this tool handle very large numbers?

Is 1 considered a prime number?

Are there infinite prime numbers?

Can this tool be used for educational purposes?