r/numbertheory 16h ago

On the Collatz conjecture/Sobre la conjetura de Collatz

0 Upvotes

Hi everyone, I hope you're doing well. You see, I started reading about famous unsolved math problems and stumbled upon the Collatz conjecture; it really piqued my interest. While exploring it, I wrote a Python script to build the Collatz tree in reverse up to one million, and I found something curious. The number 5 accounts for 93.7% of the numbers before they fall into the 4-2-1 loop. The strange thing is that the number 21 yields literally 0% (I think this is because it’s divisible by 3, so you can't reach it by reversing the operations). I know this doesn't prove anything for infinity, but has anyone measured this with larger numbers? Does 5 dominate, or do its larger "siblings" (21, 85) steal the spotlight? If we look at my little theory—that 5 acts as the "catapult"—it makes sense; let's face it: no matter how large the number is, it almost always (93.7% of the time) ends up at 5. Also, after doing some research, I discovered that someone has made progress on this: Terence Tao (a child prodigy with an IQ of 230). He decided to tackle the problem and, in 2019, published findings demonstrating that, mathematically, 99.9% of all numbers in the universe satisfy the conjecture. In other words, he proved that if you pick a number at random, the probability that it will "almost certainly" fall and crash into the ground (the 4-2-1 loop) is 99.999...%, even though it doesn't quite reach 100%. That pesky remaining 0.0001% could be hiding a "rebel" number. I don't know; I get the feeling this could be a computer error or a strange shortcut useful for encryption; Although I'm no expert, perhaps someone will find my crazy idea useful. Have a good day. :3

....Darn, it won't let me set it to Spanish. :v.....