Things you might want to consider:
- It might be risky for others to find out. Presumably your new-found knowledge is valuable to all sorts of dangerous people. Nation state level actors. Organized criminals. Suddenly shifty-looking friends and family.
- Even if they don't know who you are in the real world, you'd probably be a target for hacks and people trying to steal your tech by any means possible.
- Cryptocurrency hijinks are attractive, but it could be hard to get your gains back to fiat due to (a) the value crashing when people realize, and/or (b) it possibly being illegal to exploit your invention in this way.
- Opting for fiat directly--say, by simply selling factorizations to the highest bidder--means you'll have to deal with the banking apparatus and tax agencies. If explaining crypto gains was hard, imagine trying to un-freeze your account by explaining how un-multiplying numbers got you however many millions of dollars.
This sounds like a fun sci-fi/techno-thriller premise, so it's basically a race scenario between your ever-so-clever protagonist trying to cash in before being discovered. Crypto hijinks could include siphoning off funds from a shady-looking exchange site (so they fall under suspicion first) or quietly emptying abandoned or locked wallets. Another fun scenario is getting a low-status job in the mailroom (ie any company where your protagonist has access to lots of encrypted traffic) and making brilliant stock trades in the evening. When you get caught you show off your collection of dead tree newspapers (just the pages witht he stock listings) and pretend to be some sort of idiot savant who can perceive the mysterious underlying patterns in the market, buying a breathing space before going on the run. Better yet, pull encrypted data literally out of the air, eg encrypted FBI comms in a big city, then start a career as a mysteriously successful crime or paparazzi photographer who keeps magically turning up in the right place and selling pics for a lot of cash, which also gives and opportunityt o meet other interesting people and decrypt their secrets.
If you just want to cash in legally and retire in comfort and safety you just set up a corporation, do tech demos and sell it to the military; better yet, sell a solution to the problem you just created. You do slightly impressive tech demos and then scare the pants off the brass in person. If your protagonist is evil, invest in defense stocks, crack encrypted embassy communications from two countries that hate each other, leak the information, cash in big as they hurtle toward war.
While your knowledge is indeed valuable to dangerous people, it also provides you with the means to remain one step ahead of them right up tot he moment where they realize the nature of your unfair advantage and stop depending on encryption (but thereby incurring a speed or security setback). For an abundant source of additional ideas, try vampire stories.
As for legal things: At the very least I would submit it to bug bounty programs, maybe sell it to the NSA. If I'm still allowed to, I guess I would try writing a paper about it.
I have previous relevant experience running is is isodd.dev and iseven.dev, two SAAS that tell if a number is odd or even.
I think the bigger question is, if you had this factorizing tech, what stack would you use to implement it?
Isn't this process just called prime factorization, or is it something else?