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."
Where are you quoting this from? It's ill-defined / ambiguous as you're stating it. I'm a professional number theorist and I don't understand what your question is actually asking. Thanks!
AKS is a primality check in polynomial time, IE much faster than trial division. It's not "simple" for certain values of simple, but it's only 5 major steps.
Finding primes is a P problem though, so I'd consider it a "solved problem". There's no equation that generates nothing but primes, is that what you meant?
There are many such formulas, such as Willan's 1964 simple formula for the nth prime. But they are basically all hiding a sieve, Wilson's theorem, the prime count function, or some other calculation. That is, none of them are at all practical, and most offer no insight.
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.
If you're still within the edit timer, you should really replace this comment with "I have discovered a truly marvelous proof of this, which this margin is too narrow to contain." Maybe they'll rename the conjecture after you.
"Mathematicians have tried many different possibilities and have yet to find a single one that works. But they also haven't been able to prove that such a box doesn't exist, so the hunt is on for a perfect cuboid." apparently, something wrong here.
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[ 3.2 ms ] story [ 68.2 ms ] thread"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."
Could you provide more clarification on what's wrong?
I'd recommend perusing "Formulas for Primes" by Underwood Dudley, 1983. Free online link: http://www.maa.org/programs/faculty-and-departments/classroo...
"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.
This isn't true.
6/2 = 3
In fact. Every odd number multiplied by two is even.