Programs, Data, and Testing Results on Collatz Dynamics of Extremely Large Integers

We computed the largest integer that can return to 1, which is 6000000 bits long (currently known is 128 bits).We proposed an algorithm that can compute extremely large integer by using logical computation instead of numerical computation.We discovered that ratio of Collatz dynamics goes to 1 with the growth of starting integer.We evaluated that dynamics for sufficient large integers is random.We proposed a random bit sequence generator by only using logical computation (or gates).

我们计算出了能够回归1的最大整数，其长度为6000000比特（当前已知的最大长度为128比特）。我们提出了一种算法，通过逻辑计算而非数值计算来处理极大整数。我们发现，随着起始整数的增大，科拉茨动力学的比率趋近于1。我们评估得出，对于足够大的整数，其动力学行为具有随机性。我们提出了一种仅使用逻辑计算（或门）的随机比特序列生成器。