That is apples to oranges, you're citing a lattice reduction algorithm? Maybe you meant the number field sieve https://en.wikipedia.org/wiki/General_number_fiel

That is apples to oranges, you're citing a lattice reduction algorithm? Maybe you meant the number field sieve https://en.wikipedia.org/wiki/General_number_field_sieve https://en.wikipedia.org/wiki/General_number_field_sieve? In that case the answer is: never. We've tried to generously interpret earlier factoring annealing results (there is nothing new in the top-posted paper) and had to conclude that the overall method just doesn't scale well: https://arxiv.org/abs/1902.01448 https://arxiv.org/abs/1902.01448