Are there any properties that all primes share in common (while all the non-primes don't share it), and could be written in a simple formula which involves only 1 positive integer variable? Thank you!
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2$n$ is prime iff $n>1$ and for all natural numbers $k$ holds that if $k$ divides $n$ then $k= 1$ or $k= n$. – Ittay Weiss Mar 24 '13 at 00:02
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1no that was not what I was looking for, that is a definition of a prime number, still thank you – user1398593 Mar 24 '13 at 00:03
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1my comment was meant to force a more precise question. I did post a more serious answer though. – Ittay Weiss Mar 24 '13 at 00:05
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Wilson's Theorem: $n$ is prime iff $n>1$ and $(n-1)!=-1$ modulo $n$.
Ittay Weiss
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Thank you. I got the same result although written a bit different: n is prime iff e^(24PI( (2n choose n)-1)/n^3 )=1 This was actually the reason I was asking the question. – user1398593 Mar 24 '13 at 00:08
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just to show everyone what I initially thought was going on afterwards e^(i24PI( (2n choose n)-1)/n^3 )cos^2(PI*n)-1=0 holds for all real numbers >0 from there it's almost no problem to catch the nullpoints. – user1398593 Mar 24 '13 at 00:23