It is an interesting fact, though, since there is a sequence of integers called "integers factored by computers". This integer is now a member of that set. The fact that a number this large was factored is interesting to the mathematical community. Should this information be suppressed because TI used this number to sign their OS?

What if there was a table of all numbers and their factorizations, 1 = 1, 2 = 2, 3 = 3, 4 = 2 * 2, ... If you noticed TI was using a number in this list as their signing key, you could just look it up. Would that be illegal?

Then why is it illegal to lazily generate this list as needed?

What other properties of integers are illegal to discuss?

(FWIW, I am almost certain that the DMCA does not apply to this case, anyway. TI is just sending letters Because They Can and because there is no penalty if they're wrong. I can send you a C&D telling you to take down the above comment. The appropriate response is to mock me, not to take the comment down.)

Basically, TI should have used a bigger integer. Why rely on something as flaky as the legal system to protect your business model when you can use mathematical fact instead? (Answer: because using a bigger number would have added 1 cent to the cost of every calculator sold. Sending C&Ds is free.)

You are still playing cute and don't understand how you'll be cut off by a judge (ie., common sense) in seconds.

Sir, is that the only large number that you published? Are you saying that your interest in this number has nothing to do with its presence as a key in TI's calculators? How come a search of your house found all those dumps of TI firmware? Seriously?

Don't get me wrong, I'm on your side, but this defense is called "playing stupid" and it is known not to work.

The good news is that this will never see the inside of a courtroom, as publishing factorizations of numbers is legal. So is doing whatever you want to your own hardware.

But anyway, how hard does the math problem have to be before it becomes illegal to solve? If my signing key is 4, would it be illegal for someone to say "Gentlemen, it has come to my attention that the number 4 is the product of 2 and 2."? Why?

How is 4 different from 68575999143494039 77654744967172758 17990411426461294 73261271699761332 96980951450542789 80888450430107555 07864648023040197 95402754670660318 614966266413770127 ? (I need to know what the law is before I can try to avoid breaking it.)

Also, is the mere act of looking up the factorization of this number in a table illegal? If not, what about using a program that has the number stored in a table? If not, what if that program lazily computes the factorization. Is strict evaluation legal, but not lazy evaluation?

How about if I have a friend that randomly wants to know the factorization of a number and I compute it in my head? What if it's for breaking a cryptosystem, but I don't know that, I just think it's a problem he's challenging me with? Who broke the law? What law was broken?

Anyway, I don't think you've thought this through. You used the word "cute" dismissively, though, which was very cute...

> But anyway, how hard does the math problem have to be before it becomes illegal to solve?

Well, that is the point, isn't it. It is about intent, not the difficulty of the problem. Picking up a wallet is easy, taking someone's wallet is illegal.

But, the intent here: "use my own software on my own hardware", is (or should be) legal - all the rest is fluff.

While I agree with the general principle you're espousing, from a legal point of view, it's clearly possible to decide that the probability that someone "just happened" to factor a sufficiently large number is low enough to determine beyond reasonable doubt that they had some ulterior motive in doing so.

> How is 4 different from 68575999143494039 77654744967172758 17990411426461294 73261271699761332 96980951450542789 80888450430107555 07864648023040197 95402754670660318 614966266413770127 ? (I need to know what the law is before I can try to avoid breaking it.)

How is "Limp" different from "Limp, the body of Gorrister hung from the pink palette; unsupported—hanging high above us in the computer chamber; and it did not shiver in the chill, oily breeze that blew eternally through the main cavern. The body hung head down, attached to the underside of the palette by the sole of its right foot. It had been drained of blood through a precise incision made from ear to ear under the lantern jaw. There was no blood on the reflective surface of the metal floor. [...]"?

There might be legal precedent on this issue since there used to be books of tables of logarithms published in the days before calculators and computers. The publishers would place subtle errors in a few random points many digits out to prove that someone else had copied the numbers without computing the logarithms themselves. Of course IANAL.

Forgive me my lack of insight, but I'm not entirely certain what that has to do with this particular case. What you are listing is a mechanism for copyright protection - while the numbers themselves cannot be copyrighted, the book containing them might qualify for copyright (depending on the local legal system).

The question here is not about copyright, however. (Probably. Maybe.) The question here is whether it is legal to factor an arbitrary number and inform others of the results.

England and the United States have decided differently (england: yes, us: no) whether to allow copyright of lists of otherwise uncopyrightable information. The long term outcome has been a thought provoking natural experiment: the United States, with no such copyright allowance, has a thriving industry of competing databases of various kinds of publicly available information. The UK has no such thriving ecosystem. Or at least this was all according to a newspaper article a few years back. For all I know they may have since seen the light and banned copyright on databases.

Copying the table may be illegal (although probably not; you can copy the phonebook), but referring to it while figuring out how to make a flat screwdriver unscrew a phillips-head screw is probably not. How is using a flat screwdriver to unscrew a phillips-head screw different from using your own OS on your own calculator instead of using TI's?