Mathematical Concepts
Understanding Prime Numbers
Prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves. They are the building blocks of all integers and have fascinated mathematicians for centuries.
Key Properties of Prime Numbers:
- Fundamental Theorem: Every integer greater than 1 can be represented uniquely as a product of primes
- Infinity: There are infinitely many prime numbers (Euclid's theorem)
- Distribution: Primes become less dense as numbers get larger
- Applications: Essential in cryptography, computer science, and number theory
- Testing Methods: Various algorithms exist to test primality efficiently
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