There is absolutely no threat from a breaking change, unless someone cracks the factoring problem and can solve the hashing problem instantaneously, in which case we have bigger issues to worry about.
1) Solving the hashing problem (finding a message with SHA256 hash lower than given threshold) has nothing to do with factoring. It's RSA encryption that breaks if the factoring problem is solved. Bitcoin does use RSA and will break if the factoring problem is solved, but in completely other way.
We definitely should have economical and mathematical FAQs, because mathematical or economical nonsense appears now and then on the forum and scares new users.
2) So you message should read "unless someone can solve the hashing problem instantaneously, in which case we have bigger issues to worry about"
These "bigger issues" were already discussed somewhere at the forum, and nothing catastrophic would happen if the cryptographic functions Bitcoin depends on are broken. This again should be a FAQ.
Good answer...
Bitcoin use criminals only 0,1 %
Others people use Btc for good purposes..
Criminals use fiat currencies 😏 💱
Again...
80 % bitcoin speculation...
20 % real use for buying, selling items and other...
Many thanks for watching
Best regards
Donatas Leonavicius