Prime Number Checker
Check if numbers are prime and explore prime number properties
Check Prime Numbers
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Prime Factorization
{{ numberToCheck }} = {{ primeResult.factorization }}
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Number Properties
Divisors:
{{ primeResult.properties.divisors.join(', ') }}
Sum of Divisors:
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Even/Odd:
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Special Type:
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Prime Number Generator
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Count: {{ generatedPrimes.length }}
Density: {{ ((generatedPrimes.length / (rangeEnd - rangeStart + 1)) * 100).toFixed(1) }}%
{{ prime }}
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