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Reconstruction and Trial Verification of the Collatz Conjecture Based On Big Data

This paper redefines the Collatz conjecture and proposes the strong Collatz conjecture, which is a sufficient condition for the Collatz conjecture. Based on the computer data structure–tree, we construct a non-negative integer inheritance decimal tree. The nodes on the decimal tree correspond to non-negative integers. We further define the Collatz-leaf node (corresponding to the Collatz-leaf integer) on the decimal tree. The Collatz-leaf nodes satisfy the strong Collatz conjecture. Through mathematical derivation, we prove that the Collatz-leaf node (Collatz-leaf integer) has the characteristics of inheritance. With computer large numbers and big data calculation, we conclude that all nodes at a depth of 800 are Collatz-leaf nodes. Thus, we prove that the strong Collatz conjecture is true, and therefore the Collatz conjecture must also be true. For any positive integer N greater than 1, the minimum number of Collatz transforms from N to 1 is log2 N, the maximum number of Collatz transforms is 800 * (N-1). The non-negative integer inheritance decimal tree proposed and constructed in this paper also can be used for proofs of other mathematical problems.