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maybe you stopped your m too soon (in my case I solved stopping m a little later...)
Can you please be a bit clearer ?
the first step of my algorithm is to generate all the primitive triples and their multiples with perimeter less or equal 5*10^6 using Euclid's formula, and in first instance I assumed that m<=1200 was sufficient to generate al the triples (I've approximated n=m, so max perimeter was near 4*1200^2) but this way I was loosing some triangles generated by higher m...