Limits RegistryPUBLIC RECORDLimits RegistryPUBLIC RECORDLimits RegistryPUBLIC RECORDLimits RegistryAndrew Beal formulated this conjecture in 1993 while investigating generalizations of Fermat's Last Theorem. It asks whether every solution to A^x + B^y = C^z with all exponents greater than 2 forces A, B, and C to share a common prime factor — equivalently, that the equation has no solutions in pairwise-coprime positive integers under those exponents. It remains open and unproven.
The question, scope, and sources behind this Registry record.
If A^x + B^y = C^z, where A, B, C, x, y, and z are positive integers with x, y, z > 2, then A, B, and C have a common prime factor.
Change a parameter to stress-test whether a proposed result is still inside the published specification. This is an audit aid, not a proof checker.
Current frontiers derived from accepted Claims.
The frontier is not sacred
Most progress starts with a disagreement that survives contact with evidence. If you can push the known lower bound up or pull the upper bound down, show us the work.
≥ when you have shown that at least this value is achievable.≤ when you have shown that anything above this value is impossible.No vibes. State the value, define the scope, and link the paper, proof, code, or reproduction that lets another person check it. Editors review every challenge before the public record changes.
Challenge this recordAssertions tied to evidence, attribution, and review.
No accepted Claims are recorded for this Limit yet.
The frontier as it changed over time.
Only accepted Claims matching the current specification contribute to the displayed bounds. Strict inequalities remain open; contradictory Claims require editorial review.