5 Simple Math Problems No One Can Solve

Re:5 Simple Math Problems No One Can Solve by iamcreasy on Sunday October 16, 2016 @03:32PM (#12720489)

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."

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Re:5 Simple Math Problems No One Can Solve by YomiK on Monday October 17, 2016 @12:21PM (#12726490)

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'd recommend perusing "Formulas for Primes" by Underwood Dudley, 1983. Free online link: http://www.maa.org/programs/faculty-and-departments/classroo...

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Re:5 Simple Math Problems No One Can Solve by cyphar on Sunday October 16, 2016 @06:28PM (#12721395)

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?

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Re:5 Simple Math Problems No One Can Solve by iamcreasy on Sunday October 16, 2016 @07:17PM (#12721645)

Yes, kind of.

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Re:5 Simple Math Problems No One Can Solve by williamstein on Sunday October 16, 2016 @03:44PM (#12720544)

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!

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Re:5 Simple Math Problems No One Can Solve by hilop on Sunday October 16, 2016 @03:49PM (#12720563)

https://en.wikipedia.org/wiki/Prime_number please improve the article :-)

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Re:5 Simple Math Problems No One Can Solve by iamcreasy on Sunday October 16, 2016 @03:52PM (#12720586)

I quoted it from Wikipedia. The problem is the last line. There is no known simple formula to identify prime numbers.

Could you provide more clarification on what's wrong?

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Re:5 Simple Math Problems No One Can Solve by williamstein on Sunday October 16, 2016 @04:07PM (#12720667)

What is a "simple formula"? I have no idea what "simple formula" means. In math reseacrch everything must be 100% precise and well defined.

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Re:5 Simple Math Problems No One Can Solve by tf2manu994 on Sunday October 16, 2016 @04:10PM (#12720676)

I think they mean something a great deal faster than just dividing by each number to check.

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Re:5 Simple Math Problems No One Can Solve by SAI_Peregrinus on Sunday October 16, 2016 @09:12PM (#12722061)

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.

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Re:5 Simple Math Problems No One Can Solve by cyphar on Sunday October 16, 2016 @06:28PM (#12721397)

I think they meant there's no equation that generates nothing but primes.

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Re:5 Simple Math Problems No One Can Solve by iamcreasy on Sunday October 16, 2016 @04:30PM (#12720768)

You are correct, but I wrote it in context of the posted article.

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