5 Simple Math Problems No One Can Solve

How about the prime number problem. It's simple enough to understand.

"A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. There are infinitely many primes, as demonstrated by Euclid around 300 BC. There is no known simple formula that separates prime numbers from composite numbers."

Solved the sofa problem getting a large couch into my basement about half a year ago. Still haven't got around to fixing the drywall...

discussion on reddit.com/r/math if you are interested, highlighting various errors in the article: https://www.reddit.com/r/math/comments/57jfv7/5_simple_math_...

Put these on the wall in every classroom. (And make the kids move desks into the hall /s.)

The goal is to find a box where A² + B² + C² = G², and where all four numbers are integers: 3² + 4² + 12² = 13², except it is not the only goal.

Simple to understand. I'm surprised clickbait like this has climbed so high up on HN.

I don't really know how to prove something, but for the first problem, it seems like any odd number multiplied by any other odd number (in the example, they choose 3) will always be odd. This can/has been proven. Then, any odd number, negative or positive, with 1 added or subtracted to it, becomes even. Finally, any even number divided by two is still even and approaches two.

"Mathematicians have tried millions of numbers and they've never found a single one that didn't end up at 1 eventually. The thing is, they've never been able to prove that there isn't a special number out there that never leads to 1."

Why are they trying millions of numbers? It seems like those 3 statements are very easy to prove, and explain this "phenomenon." Also, isn't the multiplying by 3 part kind of arbitrary. It seems like the only important part to consider is that if the number is odd, add 1. The multiplying by 3 is unnecessary, and could just as easily be swapped for multiplying by any odd number.