Prime Number Knowledge
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
Prime Number Properties:
- A prime number has exactly two positive divisors: 1 and itself
- The smallest prime number is 2
- 2 is the only even prime number
- All primes greater than 3 can be written as 6k±1
- There are infinitely many prime numbers (Euclid's proof)
First 20 Prime Numbers:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71
Testing Methods:
- For small numbers: check divisibility directly
- For large numbers: optimized algorithm (check up to square root)
- This tool uses 6k±1 optimized algorithm for efficiency
Applications:
- Cryptography: RSA encryption relies on large primes
- Mathematics: Fundamental concept in number theory
- Computer Science: Hash functions, random number generation
- Competitive Programming: Common algorithmic challenge
Use Prime Checker to quickly test if a number is prime!
