This public key differs from the base point of the SECP256k1 curve quite a bit, so I assume that the private key is very small.
how can you tell that the private key is small?
It's not. A curve point being only a short distance away from the base point is not an indicator that it was multiplied only a few times.
Doubling G, and adding G to some multiple of G, completely moves away the x and y coordinates. This is the math behind doubling at least, which is done a few several dozen times for a given private key number.
First, take lambda = (3Bx2 + a)/(2By) , where (Bx, By) are the coordinates of the point B you are trying to double, and a is a parameter whose value is given along with the type of curve you are using. Since you are using the secp256k1 curve, a = 0.
So for the secp256k1 this expression becomes lambda = (3Bx2)/(2By) (I'm using red to color x coordinates and blue to color y coordinates).
Next you compute Cx = lambda2 -2Bx, then you compute Cy = lambda*(Bx - Cx) - By . And this is how you get coordinates (Cx, Cy) of the point C = B*2.
So for the secp256k1 this expression becomes lambda = (3Bx2)/(2By) (I'm using red to color x coordinates and blue to color y coordinates).
Next you compute Cx = lambda2 -2Bx, then you compute Cy = lambda*(Bx - Cx) - By . And this is how you get coordinates (Cx, Cy) of the point C = B*2.
Point addition does a similar warping of the x and y coordinates.
The very fact that you're multiplying the new points with a huge lambda implies that public key ranges do not correspond to private key ranges.
