more less I'm studying this:
to factor N = 27 * 65
you have to choose (65p) mod 8 = 0
and
you have to choose (q27) mod 8 = 0
suppose we choose 41 and 43
41 * 43 = 1763
the following W and w are in the form
W = 65 * n + (1763  27 * 65) / 8
w = 27 * m + (1763  27 * 65) / 8
(17633) / 8 = 220
220  W [4 (657) * (655) / 8] = 65 * X
W =  (65 * n + 1) = q * (65p) / 8, p * q = 1763
q = 278 * n
220  w [4 (277) * (275) / 8] = 27 * X
w = (27 * m + 1) = p * (q27) / 8, p * q = 1763
p = 658 * m
Later I test if binary search can work
Last fiddled with by Alberico Lepore on 20220103 at 15:08
Reason: update
