Number Theory & Bits
Analyze prime sieves, modular inverses, totient expansions, gray-code bits, and Diophantine solvers.
All Mathematics (15)
Prime Checker
Verify if a number is prime or composite, locate nearest primes, and check prime factors.
Sieve of Eratosthenes
Generate all prime numbers up to a specified limit N using Eratosthenes sieve algorithm.
Segmented Sieve
Generate prime numbers within a range [L, R] using optimized segmented intervals.
Prime Factorization
Decompose a positive integer N into its constituent prime factor exponents representation.
Divisors Calculator
Compute all divisors, their total count, and their summation for N.
GCD & LCM Calculator
Compute Greatest Common Divisor and Least Common Multiple for a set of values.
Extended Euclidean Solver
Compute Greatest Common Divisor and Bézout coefficients (x, y) satisfying Diophantine relations.
Modular Exponentiation
Compute modular powers (A^B) % M in logarithmic time steps.
Modular Inverse Solver
Calculate modular multiplicative inverses using Extended Euclid or Fermat's Little Theorem.
Euler Totient Solver
Compute Euler's Totient function φ(N) values and expand prime products.
Möbius Function Solver
Compute Möbius μ(N) values and determine square-free prime counts.
Chinese Remainder Theorem
Solve systems of simultaneous congruences for pairwise coprime moduli.
Bitwise Playground
Analyze logical AND, OR, XOR, NOT, and shift operations in decimal, hexadecimal, and binary configurations.
Gray Code Generator
Convert standard binary values to reflected Gray code values bidirectionally.
XOR Playground
Compute array prefix XORs, range XORs, and evaluate O(1) integer range XOR cycles.