* Any machine learning system must be involved in finding the solution directly, or finding new algorithms (in which case, new mathematics also resolves yes).
** New algorithm, lowering the computational complexity compared to currently known algorithms:
- Number field sieve, if the computations were performed on a classical computer.
- Shor's algorithm, if the computations were performed on a quantum computer.
All options may resolve No, for example if this is achieved by just scaling up computational power. The question stays open until the number is factored.
1,000It'll be new mathematics before quantum precisely because new mathatics sits at the intersection of the facts that 1. factorization is not definitely known to be in NP or co-NP, 2. they've found no proof of it after decades. Quantum has issues, a lot of marketing hype, but it has issues.