HACKER Q&A
📣 anm89

How was it known in advance that the RSA numbers were semi prime?


So the RSA team published their RSA numbers many years ago to encourage research on number theory.

The basis of the challenge was that the published numbers were known to be semiprime (having exactly two prime factors).

My question is how did they choose these numbers? Did they just arbitrarily pick large prime numbers and multiply them? Is there some way to search for semiprime numbers aside from the method I just mentioned? Or is there some reason why the numbers why the numbers they picked are especially well suited?


  👤 schoen Accepted Answer ✓
It's exactly the same as generating an RSA public key -- pick two prime numbers and multiply them. The only interesting part is that the sizes were chosen carefully to give an increasing ladder of difficulty.

There's nothing more mathematically interesting or distinctive about the RSA numbers compared to other semiprimes of similar sizes. In a way, they were meant to represent typical moduli from RSA public keys, to mimic the difficulty of attacking an RSA public key of a particular size by factoring.


👤 DoctorOetker
According to the wikipedia article "RSA Factoring Challenge":

>The RSA numbers were generated on a computer with no network connection of any kind. The computer's hard drive was subsequently destroyed so that no record would exist, anywhere, of the solution to the factoring challenge.

referring to reference 3:

https://web.archive.org/web/20130921043454/http://www.emc.co...