The thing is that it is old-washed paper and I can read only the first 9 symbols of this string.
You'll need to find a way to read the other characters. Try bright light, adjust the contrast on pictures, or get a microscope to look for damaged paper fibers. Okay, I admit, I made up that last one, I have no idea if that's possible, but it's more likely than brute-forcing the private key.
It's actually what I would try to do: use a microscope and inspect the washed out area very carefully. You don't need a lot of magnification, the ability to look at different angles on the inspection area is sometimes more important that magnification. What kind of forces did the writing tip excert to the paper, are traces of that still visible on the paper fibers.
In the end it comes down to what treatment of the paper caused the wash-out. Was it unstable colors, sunlight exposure? Did some sort of friction on the paper make any color deposit be rubbed away?
Trying to get as much of details off the paper is still a better route than trying to bruteforce into the unknown.