For a positive integer, g, let \(p(g)=g^2+g+1\). Find the largest positive integer g such that \(1000 p(1^2) p(2^2) \dotsm p(g^2) \ge p(1)^2 p(2)^2 \dotsm p(g)^2.\)
The answer is 14.
+143 
