Verifying whether extremely large integer guarantees Collatz conjecture (can return to 1 finally)

Currently, the largest integer being verified for Collatz conjecture is about 2^60 . To verify whether extremely large integers such as 2^{100000}-1 can return 1, we design a new algorithm. This dedicated algorithm can change numerical computation into bit or charter computation, hence, original dynamics for extremely large integer without upper bound can be computed. By this algorithm, we thus design computer program that can output original dynamics for extremely large integers without upper-bound such as 2^{100000}-1, which is the largest integer being verified until now. The source code is txpo15.c. The bit length of extremely large integer can be set up by Macro (named MAXLEN) in source code. The program can output the original dynamics (called CODE) of a starting integer in terms of “-” presenting (3*x+1)/2 and “0” presenting x/2. This data can be used for verifying whether extremely large number can go to 1 finally. Note that, there is no upper bound for extremely large starting integer; all is timing issue.

目前，对于柯尔查克猜想所验证的最大整数约为2的60次方。为了验证如2的100000次方减1等极大整数能否返回1，我们设计了一种新的算法。该专用算法能够将数值计算转化为位或字符计算，从而实现对于无上界极大整数的原始动力学计算。通过此算法，我们进而设计了一种计算机程序，能够输出无上界极大整数（如2的100000次方减1，目前所验证的最大整数）的原始动力学（称为CODE）。该源代码文件名为txpo15.c。在源代码中，可以通过宏（命名为MAXLEN）设置极大整数的位长度。该程序能够以“-”表示(3*x+1)/2和“0”表示x/2的形式输出起始整数的原始动力学。这些数据可用于验证极大整数最终能否达到1。请注意，起始极大整数没有上界；一切取决于计算时间。