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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?


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