Advanced Prime Number Calculator

Explore prime numbers with interactive visualizations and comprehensive analysis

🔢 Prime Checker

Check if a number is prime and explore properties

Number to Check

Operation

End Number (for range)

📊 Results

Prime number analysis

17 is PRIME

Number 17

Prime Factors 17

Next Prime 19

Previous Prime 13

📈 Prime Distribution

Prime density visualization

🎯 3D Prime Spiral

Interactive Ulam spiral visualization

Drag to rotate • Scroll to zoom
Red: Prime numbers • Blue: Composite

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 natural numbers and play a fundamental role in mathematics, cryptography, and computer science.

Definition

A prime number p > 1 has exactly two factors: 1 and p. The first few primes are 2, 3, 5, 7, 11, 13...

Fundamental Theorem

Every integer > 1 can be expressed as a unique product of prime numbers (prime factorization).

Applications

Cryptography (RSA), hash functions, random number generation, and mathematical research.