P vs NP Problem

Collatz conjecture
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This is the simple math problem we still can’t solve!!
Just pick a number (any number). If it's even, divide it by 2. If it's odd, multiply it by 3 and add 1. Take that new number and repeat the process, again and again. If you keep this up, you’ll eventually get stuck in a loop. At least, that’s what we think will happen.

Take 10 for example: 10 is even, so we cut it in half to get 5. Since 5 is odd, we triple it and add 1. Now we have 16, which is even, so we halve it to get 8, then halve that to get 4, then halve it again to get 2, and once more to get 1. Since 1 is odd, we triple it and add 1. Now we’re back at 4, and we know where this goes: 4 goes to 2 which goes to 1 which goes to 4, and so on. We’re stuck in a loop.

Or try 11: It’s odd, so we triple it and add 1. Now we have 34, which is even, so we halve it to get 17, triple that and add 1 to get 52, halve that to get 26 and again to get 13, triple that and add 1 to get 40, halve that to get 20, then 10, then 5, triple that and add 1 to get 16, and halve that to get 8, then 4, 2 and 1. And we’re stuck in the loop again. it is a mathematical black hole.

As simple as it sounds, it actually works. But the problem is that even though mathematicians have shown this is the case with millions of numbers, they haven't found any numbers out there that won't stick to the rules.

"It's possible that there's some really big number that goes to infinity instead, or maybe a number that gets stuck in a loop and never reaches 1," explains Thompson. "But no one has ever been able to prove that for certain."

If You Solve P vs NP Problem, You Could Steal All the Bitcoin in the World!
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If you can prove or disprove its cryptically short equation, you’d be a million dollars richer—and maybe even billions of dollars richer, depending on your scruples.

The importance of P versus NP is mainly in its consequences for computing. It happens to be one of the seven Millennium Prize Problems, meaning The Clay Mathematics Institute of Cambridge, Massachusetts will award $1 million to whoever manages to prove or disprove the statement. But should you prove that P in fact does equal NP, you wouldn’t even need the $1 million prize. As theoretical computer scientist Scott Aaronson explained last week at a lecture in a stuffy auditorium at Los Alamos National Lab in New Mexico, proving that P=NP would open up some intriguing possibilities.

“If someone proves P=NP, the first thing they should do is steal $200 billion in bitcoin. The second thing they should do is solve all of the other Millennium Prize Problems,” Aaronson said.

To understand this, you need to know that computers are devices that solve problems, abstracted into code readable by the physical computing device, based on the principles put forth by Alan Turing. Solving problems takes a number of steps and a certain amount of time, with the amount of time required increasing as the problem grows larger.

So go out there and try and prove that P does, or does not, equal NP. If you’re successful, you’ll make at least a million dollars, and perhaps much, much more. If you’re unsuccessful, well, hopefully you will have led a meaningful life researching computational theory.