The number 13,532,385,396,179 may sound like a random sequence of digits with no significance. However, it has surprised the mathematical community and attracted attention due to its extremely unique characteristics. This number is not just a meaningless long string, but also provides a solution to an open problem posed by the legendary mathematician John Horton Conway. So what makes it so special?
This number stands out because it directly challenges a famous conjecture by Conway regarding the “climbing” of integers. According to Conway’s conjecture, any number, when factored into its prime factors and then “reduced” by removing the exponents, will eventually reach a prime number. For example, the number 60 can be expressed as 2^2 × 3 × 5, and when the exponents are removed, we obtain the digits 2, 2, 3, and 5, which combine to form 2235. This process is repeated until a final prime number is reached. Conway’s conjecture asserts that every number will arrive at a destination that is a prime number in this journey.
The number 13,532,385,396,179 has a special and interesting property in mathematics. (Illustration).
In this context, Conway generously placed a $1,000 bet for anyone who could prove this conjecture true or false. In 2017, just when it seemed like his conjecture would stand forever, a surprising counterexample emerged: the number 13,532,385,396,179.
The number 13,532,385,396,179 possesses a unique and fascinating property in the field of mathematics, particularly in number theory. It serves as an example of a number that does not “climb” to become a prime number according to the process described by mathematician John Horton Conway. According to this process, if you take any number, such as 60, you will write out its prime factorization, which means 60 can be expressed as 2 squared times 3 times 5. Then, you “bring down” all the exponents, meaning you write 60 as 2235. If you repeat this process, you will ultimately arrive at a prime number.
The “static” climb and bizarre loop
The remarkable aspect of this number is that when applying Conway’s “climb” rule, it does not converge to a prime number but instead falls into an infinite loop. When analyzing 13,532,385,396,179 into its prime factors, we obtain factors of 13, 53, 3853, and 96179. Repeating this process brings the number back to itself without ever advancing to a prime number as originally conjectured.
Dr. Tony Padilla, a physics professor at the University of Nottingham, explained this phenomenon on Numberphile: “When you take the first step in this process, what you get is still just the original number.” This means that this number does not change but simply repeats itself. Thus, it has completely convincingly disproven Conway’s conjecture while becoming a living testament to the surprises that mathematics can offer.
This number does not change, but simply repeats itself. (Illustration).
The number 13,532,385,396,179 does not conform to this rule. When you take the first step in the “climb” process—factoring that number into its prime factors—you will end up repeating itself. This number, when analyzed for its prime factors, is 13 times 53 squared times 3853 times 96179. When you remove all the exponents, you get back the original number—and this number never changes. This has proven that it is not a prime number and serves as a counterexample to Conway’s conjecture.
The Discoverer: An Amateur Mathematician
Interestingly, the discoverer of this number is not an expert. Instead, it is James Davis—a relatively unknown figure in the mathematics community; he is simply a number enthusiast. He happened to read a blog post about Conway’s conjecture and began experimenting with numbers himself. And then, he discovered the counterexample that many mathematicians may have overlooked for years.
“He’s just a guy who enjoys playing with numbers and has a passion for seeking the truth,” Padilla shared. According to Padilla, Conway owes him $1,000 as per his promise.
This number opens a new perspective on conjectures and rules in mathematics. (Illustration).
The Significance of the Discovery
The discovery of the number 13,532,385,396,179 is not merely a numerical achievement. It opens a new perspective on conjectures and rules in mathematics, showing that what seems unchangeable can easily be shattered by a surprising counterexample. Furthermore, this serves as evidence that mathematics is not just a playground for experts; anyone with passion and curiosity can uncover great discoveries.
By transcending the limits of a conjecture once thought to be solid, the number 13,532,385,396,179 has become a symbol of the surprises and beauty of mathematics.
