Comprehensive number theory laboratory: Explore prime numbers, factorization, modular arithmetic, sequences, and advanced mathematical properties. Perfect for students, educators, cryptography enthusiasts, and math lovers.

Largest Known Prime 2⁸²ˢ⁸⁹⁹⁹³³ - 1

Digits of π

3.14159...

Primes ≤ 100

Perfect Numbers

🔍 Quick Tools:

🔢 Input Numbers & Operations

First Number (n)

Second Number (m) (optional for some operations)

⚡ Select Operation

Show Detailed Steps

Prime Check Options

Use probabilistic test (faster for large numbers)

📊 Results & Analysis

🧮

Enter numbers and select an operation

Results will appear here with detailed explanations

⭐ Number Properties

Type

Divisor Count

Digital Root

Base Conversions

🎯 Factorization Tree

🌳

Enter a number and run factorization

📈 Prime Distribution

🔢

Visualize prime number patterns

⚡ Advanced Number Theory Tools

🔐 Cryptography & RSA

Generate RSA Keys

Modular Exponentiation

📊 Number Sequences

Sequence Type

Generate up to

🔄 Base Conversion

Number to Convert

From Base

To Base

💾 Export & Educational Resources

📚 Number Theory Insights

Prime Number Theorem

π(x) ≈ x/ln(x) where π(x) is the prime-counting function.

Euclid's Algorithm

For finding GCD: gcd(a,b) = gcd(b, a mod b). Efficient for large numbers.

Fermat's Little Theorem

If p is prime and a not divisible by p, then a^(p-1) ≡ 1 mod p.