Hi James,

The code you provided formatted correctly.

prim = With[{max = 100}, 
  Map[Last, 
   List @@ (Reduce[
       x^2 + y^2 == z^2 && 0 < x < y < max && 0 < z < max && 
        GCD[x, y, z] == 1, {x, y, z}, Integers, 
       Backsubstitution -> True] /. And :> List), {2}]]

It is hundreds of times slower than genPTunder that I referred to in my previous reply.

It looks like the triples were filtered in some way to generate the image you provided. So this does not generate an identical image. It does match the image on Wikipedia.

genPTunder[6000] // Map[Most] // Join[#, Map[Reverse, #]] & //
  ListPlot[#, AspectRatio -> 1, ImageSize -> 600, PlotStyle -> Blue] &

Thanks, JP

Paul, I forgot to mention, I've already done the hard work on this notebook, just run this one, the long version, it only takes a few minutes at most: https://www.notebookarchive.org/ppt-graph-nb--2021-06-6y23baq/

JP

You may also find my method of generating PPTs useful. It generates all ppt's {a, b, c}, with the short leg as the input, where a<b<c. It is easily modified if you want all ppts with any leg equal to the input value by changing this part # > x to # > 0.

pyths[x_Integer] := (t = Select[Divisors[x^2], # <= x &]; 
  m = Sort[Select[(x^2 - t^2)/(2 t), IntegerQ[#] && # > x &]]; 
  Table[{x, m[[i]], Sqrt[x^2 + m[[i]]^2]}, {i, 1, Length[m]}])

or primitive ppt's

primpyths[x_Integer] := (t = Select[Divisors[x^2], # <= x &]; 
  m = Sort[Select[(x^2 - t^2)/(2 t), 
     IntegerQ[#] && # > x && GCD[x, #] == 1 &]]; 
  Table[{x, m[[i]], Sqrt[x^2 + m[[i]]^2]}, {i, 1, Length[m]}])

pyths[1000]

{{1000, 1050, 1450}, {1000, 1875, 2125}, {1000, 2400, 2600}, {1000, 
  3045, 3205}, {1000, 4950, 5050}, {1000, 6210, 6290}, {1000, 9975, 
  10025}, {1000, 12480, 12520}, {1000, 15609, 15641}, {1000, 24990, 
  25010}, {1000, 31242, 31258}, {1000, 49995, 50005}, {1000, 62496, 
  62504}, {1000, 124998, 125002}, {1000, 249999, 250001}}

primpyths[1000]

{{1000, 15609, 15641}, {1000, 249999, 250001}}

Thanks, I'm not familiar with genPTunder. I'll look into it. Your graph looks like you have all Pythagorean triples, not just the primitive ones.