Carmichael Lambda Function Calculator

Compute each prime-power Carmichael value, apply the special power-of-two rule, and take their least common multiple. Powers of two at exponent three or greater use 2^(a-2), not Euler's full totient. Inputs must be whole numbers inside the displayed safe bound. The calculator does not round decimals into the domain or silently substitute a different convention, so verify each entered integer before interpreting the exact result.

Lambda divides Euler's totient and controls a universal exponent; an individual residue can have a smaller multiplicative order. Test coprime residues by modular exponentiation; the reported exponent must return one for each. Use the displayed factors, recurrence step, or modular residue as an independent check. Exact integer output means the implemented arithmetic has no decimal approximation within its bound; it does not prove an unrelated theorem or an unstated combinatorial model.

This transparent bounded calculator is for number-theory study, not production key generation or cryptographic validation. Security depends on large secret parameters and vetted constant-time libraries far beyond this browser demonstration. The bound keeps browser work predictable and every returned integer within JavaScript's exact safe range. Larger inputs need arbitrary-precision software, explicit resource controls, and independent verification rather than treating an overflowed floating-point value as exact.