I need to find RSA private key $(d, N)$ knowing $(e, N)$. It's "own" RSA implementation. As i know
$p$ is random 70 bit number, then $q$ is $p-2^{10} < q < p+2^{10}$
$d$ is max 16 bit long with low number of ones in binary representation.
$e= 4223234360740816682261885795416553301541344119$
$N = 5074772291286459206774040208059072021046562917$
I tried to use Wiener's_attack with implementation from GitHub.
It gives me $d = 1031$. Is it the answer ? How to check if is it valid ?
What are the right ways to find d ?