To factorize N = p * q with p < q e (p-2) mod 9 = 0, there are a set of equations. These equations can be put into any popular math solver, in order to gain access to the primes p and q. For instance, the prime components of the public key N = 209 can be solved as follows:
[(h+1)^2]*[(2*h+2)^2/2-1] = X*(209-4-2*n+2*(p-2)),(h+1)/3=(k+1)/6 ,p^2+n*p=209,
h+1+k+1=(209-4-2*n+2*(p-2)),h,X,n,k
->
h = (2 (-209 + 99 p + 2 p^2))/(3 p)
[(h+1)^2]*[(2*h+2)^2/2-1] = X*(209-4-2*n),(h+1)/3=(k+1)/6 ,p^2+n*p=209,
h+1+k+1=(209-4-2*n),h,X,n,k
->
h=(2 (-209 + 101 p + p^2))/(3 p)
(2 (-209 + 99 p + 2 p^2))/(3 p)-(2 (-209 + 101 p + p^2))/(3 p)=6
->
p=11
This shows that p = 11. By simple division, it can be determined that q = 19.
It seems to me as if this approach is somewhat obvious, and I'd like to know how RSA is still considered secure if I can do these calculations in a math solver?