1. Using C Programming Language to
prove the Collatz Conjecture for
extremely large numbers
By: Yused Valentina Rodríguez
American Military Academy
Mentor: Joseph Colón
Assistant mentor: Valerie Ann
Carrasquillo
Universidad Metropolitana
Bio-Mathemathics

2. Outline
Abstract Slide 3
Introduction Slide 4
Study Area Slide 5
Procedure Slide 6
Results Slides 7 and 8
Proposition Slides 9 and 10
Conclusion Slide 11
Future Works Slide 12
References Slide 13
Acknowledgements Slide 14

3. Abstract
The Collatz Conjecture, also known as the 3n+1 theory, is
an unproven theory proposed by Lothar Collatz. It states that by
using two simple functions (3n+1 for odd numbers and n/2 for
even numbers), the outcome will ultimately be 1. This project
involves using a different method to demonstrate the validity of
said Conjecture. The goal of this investigation is to use C
Programming Language, a general-purpose programming
language, and a specific pseudo code made for this experiment in
particular, to demonstrate the Collatz Conjecture with extremely
large numbers. The chosen numbers will be tested on a high-
functioning computer equipped with precise programming to see
if they are, or they’re not, solutions to the Conjecture.

4. Introduction

5. Study Area

6. Procedure
1. Understand C Programming Language.
2. Create a working pseudocode for the Collatz
Conjecture.
3. Turn the pseudocode into a source code.
4. Test code.
5. Record findings.

7. Results

8. Results
Iterations for 112 Iterations for 75

9. Proposition
For the code to properly run with the overly large
numbers , a mechanism that divides the number into equal, or
similar, parts will be developed and placed to work alongside the
code.
This mechanism is also known as “parallel computing”,
which means that the different parts of the number will be
worked on simultaneously as if they were single numbers.
After the process is done to the segments of the number,
each segment will be put side by side to create the total outcome
of the original large number.

11. Future Works
In the future, I hope to pursue further study in Bio-Mathematics
and Programming, and run the code developed in this
investigation with extremely large numbers on a super computer.

12. Conclusions
After analyzing the Collatz Conjecture, a code was made
that could run a number and apply the functions to determine
whether or not that number stayed true to the Conjecture. But due
to the immensity of the numbers, a mechanism to divide them
into parts and work with those segments individually was
created. Said mechanism will be applied with the code to the
Collatz Conjecture in a further investigation.

13. References
• C Tutorial. (n.d.). - Learn C. Retrieved March 15, 2014, from
http://www.cprogramming.com/tutorial/c-tutorial.html
• C Tutorial – for loop, while loop, break and continue. (n.d.).
CodingUnit Programming Tutorials. Retrieved March 15,
2014, from http://www.codingunit.com/c-tutorial-for-loop-
while-loop-break-and-continue
• C Tutorial – printf, Format Specifiers, Format Conversions
and Formatted Output. (n.d.). CodingUnit Programming
Tutorials. Retrieved March 15, 2014, from
http://www.codingunit.com/printf-format-specifiers-format-
conversions-and-formatted-output

14. Acknowledgements
• Dr. Juan F. Arratia
– Executive Director of
Student Research Development Center
• Wanda Rodriguez
– IM Coordinator
• Joseph Colón Villers
– Mentor
• Valerie Ann Carrasquillo
– Assistant Mentor
• AGMUS Institute of Mathematics

15. Thank you