🧮 Advanced Number Theory Toolkit
🧮 Advanced Number Theory Toolkit
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
25
Perfect Numbers
4
🔍 Quick Tools:
🔢 Input Numbers & Operations
⚡ Select Operation
Prime Check Options
📊 Results & Analysis
🧮
Enter numbers and select an operation
Results will appear here with detailed explanations
⭐ Number Properties
Type
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Divisor Count
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Digital Root
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Base Conversions
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🎯 Factorization Tree
🌳
Enter a number and run factorization
📈 Prime Distribution
🔢
Visualize prime number patterns
📚 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.
Perfect Numbers
Numbers equal to sum of proper divisors (6, 28, 496, 8128...).