Prime Number Checker

Check if numbers are prime and explore prime number properties

📖 Learn more in our complete guide

Check Prime Numbers

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Prime Factorization

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Number Properties

Divisors: {{ primeResult.properties.divisors.join(', ') }}
Sum of Divisors: {{ primeResult.properties.sumOfDivisors }}
Even/Odd: {{ primeResult.properties.evenOdd }}
Special Type: {{ primeResult.properties.specialType }}

Prime Number Generator

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Count: {{ generatedPrimes.length }} Density: {{ ((generatedPrimes.length / (rangeEnd - rangeStart + 1)) * 100).toFixed(1) }}%
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Showing first 100 primes. Total: {{ generatedPrimes.length }}

Prime Number Facts

What are Prime Numbers?

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...

Interesting Facts

  • 2 is the only even prime number
  • There are infinitely many prime numbers
  • The largest known prime has over 24 million digits
  • Twin primes are pairs differing by 2 (like 11, 13)

Special Prime Types

  • Mersenne Primes: 2ⁿ - 1 (e.g., 3, 7, 31)
  • Fermat Primes: 2^(2ⁿ) + 1 (e.g., 3, 5, 17)
  • Sophie Germain: p where 2p + 1 is also prime
  • Safe Primes: 2q + 1 where q is prime

Applications

  • Cryptography and security (RSA encryption)
  • Hash functions and data integrity
  • Pseudorandom number generation
  • Computer science algorithms

Notable Prime Numbers

2
The Only Even Prime
The smallest and only even prime number
101
Palindromic Prime
Reads the same forwards and backwards
1,009
First 4-Digit Prime
The smallest prime with 4 digits
2,147,483,647
Mersenne Prime M₃₁
2³¹ - 1, largest prime in 32-bit systems