The Collatz 3n+1 Conjecture Is Unprovable
نویسندگان
چکیده
In this paper, we show that any proof of the Collatz 3n + 1 Conjecture must have an infinite number of lines. Therefore, no formal proof is possible. We also discuss whether the proof strategy in this paper has any promise for proving that the Riemann Hypothesis is also unprovable.
منابع مشابه
2 9 Se p 20 04 The Collatz 3 n + 1 Conjecture is Unprovable
The Collatz 3n+ 1 Conjecture states that for each n ∈ N, there exists an m ∈ N such that T (n) = 1, where T (n) is the function T iteratively applied m times to n. As of September 4, 2003, the conjecture has been verified for all positive integers up to 224× 2 ≈ 2.52× 10 (Roosendaal, 2003+). Furthermore, one can give a heuristic probabilistic argument (Crandall, 1978) that since every iterate o...
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