The practical record for Shor's algorithm is definitely 3x5 = 15. A different style of quantum computer factorized 143 using another method, which seems to have

The practical record for Shor's algorithm is definitely 3x5 = 15. A different style of quantum computer factorized 143 using another method, which seems to have also have theoretical complications in addition to practical ones. It is definitely possible to factor some larger numbers than using "just Shor" but from what I understand, these methods are just "hacks" in the sense that they are not a good way to factorize in the general case. Maybe someone can correct me on this.