Prime Segment Diagram; why the codes run very slowly?

*To*: mathgroup at smc.vnet.net*Subject*: [mg106965] Prime Segment Diagram; why the codes run very slowly?*From*: a boy <a.dozy.boy at gmail.com>*Date*: Fri, 29 Jan 2010 07:49:45 -0500 (EST)

2010-01-29 Suppose p[i] is the i-th prime. Start from coordinate origin (0,0) , first line to (2,0), then line to (2,3), then to (2+5,3), then to (7,3+7), then to (7+11,10), and so go on...... here 2,3,5,7,11 is the prime list. I call this Prime Segment Diagram. It is very interest! Conjecture: The line y=x intersect with every segment of Prime Segment Diagram. It implies the balance of prime distribution. In[139]:= point[0] = {0, 0}; point[n_] := If[OddQ[n], {point[n - 1][[1]] + Prime[n], point[n - 1][[2]]}, {point[n - 1][[1]], point[n - 1][[2]] + Prime [n]}] n = 22; point[n] Graphics[{Green, Line[Table[point[i], {i, 1, n}]], Blue, Line[{{0, 0}, {point[n][[1]], point[n][[1]]}}]}, Axes -> True] why these simple codes run very slowly when n>20? how to optimize?