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Why is factorization hard, yet generating primes easy? Where do we go from here?

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I'm most interested in how encryption happens in practice, and maybe some of RSAs problems when implemented. Great Videos!

MusicBent

Correct, remember though, I said "based on our current understanding". At this point I'm assuming we know nothing about time complexity. So the factorization line is only harder by some constant factor. I didn't draw it as a different shape. If you watch random algorithms video, I explain the subtle point that we actually don't need to prove primality (just 'yes' with certainty) - then I'll show how this changes the shape of primality - and how/why constant factors don't matter

KhanAcademyLabs

Testing whether a number is prime is not easier because it only has to find one factor, but because it does not have to find any factor; it only has to answer "yes" or "no". If finding one factor was easy, one could easily break RSA: The number you want to factor there has only two prime factors. So once you found one of them, you get the other one by a simple division.

ChristianMatt

Fractal Compression erm... I mean the way things are composed, pseudo-randomly, I am actually working on a pseudo-random generator of numbers, but more in predicting numbers, Hopefully I haven't started an arms races in understanding the fractal nature of reality :3

Obito

how would you use the random # generator to find primes on the mars rovers?
I think it has to do with random # trial division.

mrcrazymadwhat

did you read my comments? the video shows N=? which indicate asking people what N is.

mwtakeru

exactly N = factorization?. Sorry if the notation confused you

KhanAcademyLabs

at 44" did you mean to say "P1 and P2=?" instead of "N=?" since you just provided N and asking people to factor P1 and P2, which is hard :-)

mwtakeru

Don't share anything to anyone, everyone wants to steal information on primes by abusing of your hypothetical knowledge on the subject.
The world is a wild place.

AdrianReef

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