Computational verification
The argument
Because every starting value up to 2^71 has been checked to reach 1, no counterexample exists below that bound, and since any nontrivial cycle would have to contain an integer larger than every verified value, cycle-length arguments (Steiner, Simons and de Weger, Hercher) force such a cycle to have more than about 10^11 elements; the absence of counterexamples across this range supports the conjecture.
Does it work?
Not yet evaluated.
Premises
- UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →Every positive integer up to 2^71 has a Collatz orbit reaching 1, verified by computation.
Where it is made
Passages where sources make, criticize or mention this argument. They record where it appears, not how strong it is, and none has precedence over another.
No source is recorded as making it.
Earlier ratings
- Sep 16, 2026
Granting that every starting value up to 2^71 reaches 1, the inference to the full conjecture is inductive: the verified range is a vanishing fraction of the integers, and heuristically plausible conjectures have failed at values far beyond any computation. The argument's firmest contribution is indirect, since the verified range feeds the cycle-length bounds that make a nontrivial cycle extremely constrained; it says little about a possible divergent orbit, which is where informed doubt concentrates.