gistfile1.txt

basis = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 }

46 PTs with legs < 10^9 are listed below.

        {0,1,0,1,1,1,1,1,0,1,0,0} -- this coloring scheme avoids mono-coloring all 46 PTs
                                     (parity of [dot product of this with vector-form of number] determines the number's color)

---
     12 {2,1,0,0,0,0,0,0,0,0,0,0}
     35 {0,0,1,1,0,0,0,0,0,0,0,0}
     37 {0,0,0,0,0,0,0,0,0,0,0,1}
---
     12 {2,1,0,0,0,0,0,0,0,0,0,0}
      5 {0,0,1,0,0,0,0,0,0,0,0,0}
     13 {0,0,0,0,0,1,0,0,0,0,0,0}
---
    132 {2,1,0,0,1,0,0,0,0,0,0,0}
    475 {0,0,2,0,0,0,0,1,0,0,0,0}
    493 {0,0,0,0,0,0,1,0,0,1,0,0}
---
     84 {2,1,0,1,0,0,0,0,0,0,0,0}
     13 {0,0,0,0,0,1,0,0,0,0,0,0}
     85 {0,0,1,0,0,0,1,0,0,0,0,0}
---
    204 {2,1,0,0,0,0,1,0,0,0,0,0}
    253 {0,0,0,0,1,0,0,0,1,0,0,0}
    325 {0,0,2,0,0,1,0,0,0,0,0,0}
---
    828 {2,2,0,0,0,0,0,0,1,0,0,0}
   2035 {0,0,1,0,1,0,0,0,0,0,0,1}
   2197 {0,0,0,0,0,3,0,0,0,0,0,0}
---
    468 {2,2,0,0,0,1,0,0,0,0,0,0}
    155 {0,0,1,0,0,0,0,0,0,0,1,0}
    493 {0,0,0,0,0,0,1,0,0,1,0,0}
---
     36 {2,2,0,0,0,0,0,0,0,0,0,0}
     77 {0,0,0,1,1,0,0,0,0,0,0,0}
     85 {0,0,1,0,0,0,1,0,0,0,0,0}
---
     36 {2,2,0,0,0,0,0,0,0,0,0,0}
    323 {0,0,0,0,0,0,1,1,0,0,0,0}
    325 {0,0,2,0,0,1,0,0,0,0,0,0}
---
    220 {2,0,1,0,1,0,0,0,0,0,0,0}
     21 {0,1,0,1,0,0,0,0,0,0,0,0}
    221 {0,0,0,0,0,1,1,0,0,0,0,0}
---
     20 {2,0,1,0,0,0,0,0,0,0,0,0}
     21 {0,1,0,1,0,0,0,0,0,0,0,0}
     29 {0,0,0,0,0,0,0,0,0,1,0,0}
---
    460 {2,0,1,0,0,0,0,0,1,0,0,0}
    429 {0,1,0,0,1,1,0,0,0,0,0,0}
    629 {0,0,0,0,0,0,1,0,0,0,0,1}
---
    364 {2,0,0,1,0,1,0,0,0,0,0,0}
    627 {0,1,0,0,1,0,0,1,0,0,0,0}
    725 {0,0,2,0,0,0,0,0,0,1,0,0}
---
   2356 {2,0,0,0,0,0,0,1,0,0,1,0}
    483 {0,1,0,1,0,0,0,0,1,0,0,0}
   2405 {0,0,1,0,0,1,0,0,0,0,0,1}
---
     76 {2,0,0,0,0,0,0,1,0,0,0,0}
   1443 {0,1,0,0,0,1,0,0,0,0,0,1}
   1445 {0,0,1,0,0,0,2,0,0,0,0,0}
---
      4 {2,0,0,0,0,0,0,0,0,0,0,0}
      3 {0,1,0,0,0,0,0,0,0,0,0,0}
      5 {0,0,1,0,0,0,0,0,0,0,0,0}
---
    140 {2,0,1,1,0,0,0,0,0,0,0,0}
    171 {0,2,0,0,0,0,0,1,0,0,0,0}
    221 {0,0,0,0,0,1,1,0,0,0,0,0}
---
   4900 {2,0,2,2,0,0,0,0,0,0,0,0}
     99 {0,2,0,0,1,0,0,0,0,0,0,0}
   4901 {0,0,0,0,0,2,0,0,0,1,0,0}
---
    644 {2,0,0,1,0,0,0,0,1,0,0,0}
    333 {0,2,0,0,0,0,0,0,0,0,0,1}
    725 {0,0,2,0,0,0,0,0,0,1,0,0}
---
   1564 {2,0,0,0,0,0,1,0,1,0,0,0}
   1827 {0,2,0,1,0,0,0,0,0,1,0,0}
   2405 {0,0,1,0,0,1,0,0,0,0,0,1}
---
     44 {2,0,0,0,1,0,0,0,0,0,0,0}
    117 {0,2,0,0,0,1,0,0,0,0,0,0}
    125 {0,0,3,0,0,0,0,0,0,0,0,0}
---
    100 {2,0,2,0,0,0,0,0,0,0,0,0}
    621 {0,3,0,0,0,0,0,0,1,0,0,0}
    629 {0,0,0,0,0,0,1,0,0,0,0,1}
---
    116 {2,0,0,0,0,0,0,0,0,1,0,0}
    837 {0,3,0,0,0,0,0,0,0,0,1,0}
    845 {0,0,1,0,0,2,0,0,0,0,0,0}
---
    120 {3,1,1,0,0,0,0,0,0,0,0,0}
    119 {0,0,0,1,0,0,1,0,0,0,0,0}
    169 {0,0,0,0,0,2,0,0,0,0,0,0}
---
     24 {3,1,0,0,0,0,0,0,0,0,0,0}
      7 {0,0,0,1,0,0,0,0,0,0,0,0}
     25 {0,0,2,0,0,0,0,0,0,0,0,0}
---
    264 {3,1,0,0,1,0,0,0,0,0,0,0}
   1073 {0,0,0,0,0,0,0,0,0,1,0,1}
   1105 {0,0,1,0,0,1,1,0,0,0,0,0}
---
     24 {3,1,0,0,0,0,0,0,0,0,0,0}
    143 {0,0,0,0,1,1,0,0,0,0,0,0}
    145 {0,0,1,0,0,0,0,0,0,1,0,0}
---
    360 {3,2,1,0,0,0,0,0,0,0,0,0}
    319 {0,0,0,0,1,0,0,0,0,1,0,0}
    481 {0,0,0,0,0,1,0,0,0,0,0,1}
---
    152 {3,0,0,0,0,0,0,1,0,0,0,0}
    345 {0,1,1,0,0,0,0,0,1,0,0,0}
    377 {0,0,0,0,0,1,0,0,0,1,0,0}
---
      8 {3,0,0,0,0,0,0,0,0,0,0,0}
     15 {0,1,1,0,0,0,0,0,0,0,0,0}
     17 {0,0,0,0,0,0,1,0,0,0,0,0}
---
     56 {3,0,0,1,0,0,0,0,0,0,0,0}
     33 {0,1,0,0,1,0,0,0,0,0,0,0}
     65 {0,0,1,0,0,1,0,0,0,0,0,0}
---
   1624 {3,0,0,1,0,0,0,0,0,1,0,0}
     57 {0,1,0,0,0,0,0,1,0,0,0,0}
   1625 {0,0,3,0,0,1,0,0,0,0,0,0}
---
    952 {3,0,0,1,0,0,1,0,0,0,0,0}
    495 {0,2,1,0,1,0,0,0,0,0,0,0}
   1073 {0,0,0,0,0,0,0,0,0,1,0,1}
---
    104 {3,0,0,0,0,1,0,0,0,0,0,0}
    153 {0,2,0,0,0,0,1,0,0,0,0,0}
    185 {0,0,1,0,0,0,0,0,0,0,0,1}
---
   7448 {3,0,0,2,0,0,0,1,0,0,0,0}
   3375 {0,3,3,0,0,0,0,0,0,0,0,0}
   8177 {0,0,0,0,0,1,1,0,0,0,0,1}
---
    240 {4,1,1,0,0,0,0,0,0,0,0,0}
    161 {0,0,0,1,0,0,0,0,1,0,0,0}
    289 {0,0,0,0,0,0,2,0,0,0,0,0}
---
    336 {4,1,0,1,0,0,0,0,0,0,0,0}
    527 {0,0,0,0,0,0,1,0,0,0,1,0}
    625 {0,0,4,0,0,0,0,0,0,0,0,0}
---
    144 {4,2,0,0,0,0,0,0,0,0,0,0}
     17 {0,0,0,0,0,0,1,0,0,0,0,0}
    145 {0,0,1,0,0,0,0,0,0,1,0,0}
---
    176 {4,0,0,0,1,0,0,0,0,0,0,0}
     57 {0,1,0,0,0,0,0,1,0,0,0,0}
    185 {0,0,1,0,0,0,0,0,0,0,0,1}
---
     16 {4,0,0,0,0,0,0,0,0,0,0,0}
     63 {0,2,0,1,0,0,0,0,0,0,0,0}
     65 {0,0,1,0,0,1,0,0,0,0,0,0}
---
    304 {4,0,0,0,0,0,0,1,0,0,0,0}
    297 {0,3,0,0,1,0,0,0,0,0,0,0}
    425 {0,0,2,0,0,0,1,0,0,0,0,0}
---
    480 {5,1,1,0,0,0,0,0,0,0,0,0}
     31 {0,0,0,0,0,0,0,0,0,0,1,0}
    481 {0,0,0,0,0,1,0,0,0,0,0,1}
---
   2784 {5,1,0,0,0,0,0,0,0,1,0,0}
   1463 {0,0,0,1,1,0,0,1,0,0,0,0}
   3145 {0,0,1,0,0,0,1,0,0,0,0,1}
---
    416 {5,0,0,0,0,1,0,0,0,0,0,0}
     87 {0,1,0,0,0,0,0,0,0,1,0,0}
    425 {0,0,2,0,0,0,1,0,0,0,0,0}
---
    352 {5,0,0,0,1,0,0,0,0,0,0,0}
    135 {0,3,1,0,0,0,0,0,0,0,0,0}
    377 {0,0,0,0,0,1,0,0,0,1,0,0}
---
    448 {6,0,0,1,0,0,0,0,0,0,0,0}
    975 {0,1,2,0,0,1,0,0,0,0,0,0}
   1073 {0,0,0,0,0,0,0,0,0,1,0,1}