Comment by Pazzaz

No one is "already using Shor's algorithm". Wikipedia lists the largest numbers factored using Shor's algorithm on a real quantum computer as follows:

- The number 15 (5*3) was factored in 2001

- The number 21 (7*3) was factored in 2012

- An attempt to factor 35 (5*7) was made in 2019 but they didn't succeed because of accumulation of errors in the quantum computer.

Quantum computers today are very bad, so changing the algorithm probably won't change much.