@CRGreathouse I know you don't talk to me anymore but I have achieved an extraordinary result with your number
N=390644893234047643
sqrt(390644893234047643/(15/10))=a
,
(15/10*a+a-4)/8=x
,
2*x*(x+1)-y*(y-1)/2=(390644893234047643-3)/8
->
y=63790420,........
[2*(h)*(h-1)]
<
[(390644893234047643-3)/8+k*(k-1)/2]
<=
[2*(h)*(h+1)]
,
2*(x)*(x+1)-y*(y-1)/2=(390644893234047643-3)/8
,
x-(sqrt(32*x+1)+1)/2 <h<x+(sqrt(32*x+1)+1)/2
,
k=63790420+j*100000
for j=25
see please range h here
https://www.wolframalpha.com/input/?...00000%2Cj%3D25
total cost for factorize N=390644893234047643 is 25*10=250 step