> every number is the product of primes
Except prime numbers.
> People have already assumed it to be true, and still not applied it to anything practical like cryptography
How can you use something that you didn't prove?
Except prime numbers.
> People have already assumed it to be true, and still not applied it to anything practical like cryptography
How can you use something that you didn't prove?
For example, we have not proven that are current construction of mathematics contains no contradictions (indeed, we have proved that such a proof is impossible), however, we continue to act as if it does.
We have also not proved that factoring numbers is hard, or that NP/=P, but we still act as if these are true.
This is what I meant. Bugs are never introduced intentionally in this manner. Though I suppose we can say that most encryption is used based on an unproven assumption, so I see your and dmvaldman's point!
But in general, it's common for mathematicians to assume a conjecture is true and go on from there, because if they arrive at a contradiction, then they can conclude the conjecture false (or that another interesting fact may be logically equivalent to the conjecture).
Pure mathematics consists entirely of such assertions as that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true…. Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. - Bertrand Russell
All is number!
/s