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

Citation Author(s):
Wei Ren
Submitted by:
Wei Ren
Last updated:
Thu, 11/08/2018 - 10:34
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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. 


Step 1: Configuring following code in source code of txpo15.c, which is macro in C as follows:


#define MAXLEN 100  //the maximal bit length, e.g., 100000, 1000000.


txpo15.c. It is source code in C that can be compiled into a executable program by any C compiler. It is ANSI C code, thus it can be complied for either Windows or Linux platform.


Step 2: Compile txpo15.c to generate txpo15.exe.


txpo15.exe is an executable program, and can be executed in any DOS command shell in Windows (if compiled for Windows platform) and computing results (as generated files) will be obtained. 


Step 3: Run txpo15.exe, generate following data:


1. CODE. The file is generated by running the program (i.e., txpo15.exe), and it stores dynamics data in terms of ``-'' presenting (3x+1)/2 and ``0'' presenting x/2. The counts on the

number of ''-'' and ''0'' are also included in the file.

2. input_start. The file is generated by running the program, and it stores tested starting integer that is determined by 2^{MAXLEN}-1, e.g., 2^{100000}-1.

3. DYNAMICS. The file is generated by running the program, which records all intermediate results (transformed integers), after occurring either (3x+1)/2 or x/2, from the starting integer to 1. Note that, we suggest to stop outputting this file JUST for saving time; it can be used for check the results for small starting integers such as less then 2^30-1.