Why 13532385396179 Is a Magic Number

Why 13532385396179 Is a Magic Number

Way up in the trillions, lost among so many very big numbers, lurks a hidden gem. It’s 13532385396179, or written out: thirteen trillion, five hundred and thirty-two billion, three hundred and eighty-five million, three hundred and ninety-six thousand, one hundred seventy-nine.

What’s so great about it? Watch the great video from Numberphile.

If you do the prime factorization of 13532385396179, you get 13 x 532 x 3853 x 96179. And if you look at those two things next to each other, you might notice that the digits that make up the prime factorization of our big ol’ number are the same digits that are in the number itself. If you have a hard time visualizing it, watch the clip. It’s a bit easier when the professor is drawing it for you.

This isn’t just a neat math fact. It’s also the solution to a $1,000 puzzle put forth by a mathematician. John Conway proposed that you could take a number, do its prime factorization, and then bring down the exponents (like we’ve done here with the 2 in 532). By doing so, you get a new number to run through the same process. Conway proposed that you’d always end up getting to a prime number. It’s one of those things in math that appeared to be true based on numerous examples but was difficult to prove.

But then, this week, an amateur came up with 13532385396179. This number doesn’t end up reaching a prime. Instead, you reach a loop, which disproves Conway’s conjecture. Since the prime factorization is 13 x 532 x 3853 x 96179, applying Conway’s process yields the same number you started with.



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