
Ask HN: How was it known in advance that the RSA numbers were semi prime? - anm89
So the RSA team published their RSA numbers many years ago to encourage research on number theory.<p>The basis of the challenge was that the published numbers were known to be semiprime (having exactly two prime factors).<p>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?
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schoen
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.

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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...](https://web.archive.org/web/20130921043454/http://www.emc.com/emc-
plus/rsa-labs/historical/the-rsa-factoring-challenge-faq.htm#)

