Mathematics has many open conjectures which are ridiculously hard to even understand. But this is not always the case. An example is:

- Collatz conjecture.

I would like to see some more examples. So my question is:

What are some easy to explain conjectures which are very hard to prove and unsolved?

Like most big list questions, please include one conjecture per answer. Most of the big list questions have many answers, so, for the sake of convenience of the reader who wants to read all the answers, I am including the answers:

- Goldbach's conjecture. It states that every even integer greater than 2 can be expressed as a sum of two primes.
- Twin prime conjecture: There are infinitely many twin primes.

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