According to the Richard Nordquist (http://grammar.about.com/od/il/g/impersent09.htm)
“An imperative sentence typically begins with the base form of a verb, as in “Go now!” . The implied subject “you” is said to be elliptical. ”
Hence , “Show the proof.” is an imperative .
Q.E.D.
Prime Number Formula 
Show the proof.
Proof :
According to the Richard Nordquist (http://grammar.about.com/od/il/g/impersent09.htm)
“An imperative sentence typically begins with the base form of a verb, as in “Go now!” . The implied subject “you” is said to be elliptical. ”
Hence , “Show the proof.” is an imperative .
Q.E.D.
Hi,
Checked your formula in Matlab code for n up to 115 and works pretty good!
False answers are given for the following n:
n=49 -> p(49)=227, formula(49)=229
n=98 -> p(98)=521, formula(98)=523
n=103 -> p(103)=563, formula(103)=569
n=107 -> p(103)=587, formula(103)=593
Note: In those “false” cases, your formula gives the (n+1)th prime, instead of the (n)th prime.
Overall: Impressive formula!
Is it possible to get in contact with you?
Try to run this maxima code :
n:49;1+sum((1-floor((1/n)*sum(ceiling((3-sum(floor((floor(j/i))/(ceiling(j/i))),i,1,j))/j),j,2,k))),k,1,2*(floor(n*log(n))+1));
It should work fine . You probably have to set precision in Matlab to arbitrary .