# Tag Info

There are some good reasons why this hasn't been tried. Firstly, it's not "discrete boundaries" but all points with integer coordinates $(x,y)$ on the hyperbola $xy=N$ which are candidates for factorization. The only information that matters is in those points, it doesn't matter if one uses your $$(N-xy)^2$$ and look for zeroes, or if one uses $$... 0 Mathematically, yes, it will work. Practically, you will require an extremely very long time and an incredible amount of energy, considering the sizes of the primes involved in RSA (usually around 1024-bit prime numbers). It is about billion and billions of years and billions and billions times the energy of the whole universe (RSA: How effective is this ... 4 The fancy name for this is factorization with an implicit hint. If the primes are unbalanced, i.e., if \log_2 p_i > 2 \log_2 q_i, we know how to factor n_1 and n_2 quite easily. Let k be the number of bits p_1 and p_2 differ by (a very small k, usually, for (p, p+2)); reduce the following lattice$$ \begin{pmatrix} 2^k & 0 & n_2 ...