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Aren't large non-primes usually created by multiplying two large but smaller primes together. Factoring is then the challenge. Or is there more to this that I'm missing?

The question is whether they:

a) knew it was non-prime, and used it to weaken the crypto

b) knew it was non-prime, and used it because they didn't think it needed to be prime (which is a massive sin of ignorance)

c) grabbed 1024 bits of rand() and didn't check if it was prime (again, stupid)

d) grabbed some rand and checked the prime-ness using a bad method

e) used a "prime number generator" that produced bad output

I agree that making non-prime numbers is not terribly difficult, but the question of how they got the number is only interesting in that it gives info about why.

f) Used a machine with bad RAM that flipped a bit.

This case could actually be tested for - see if any of the one-bit differences from the number used are prime.

A bit could have been flipped in the software or the result of the function (true/false), but in the number itself there appear to be no single bit flips that make it prime (at least in the binary representation).

Edit: A single bit flip could have been used as "semi" plausible deniability in the case of malicious intent.

Then again, this is wholly academic. It's not like, if it's A, the committer is going to say "yup im NSA u caught me lol."

it is the same clear path as unix vs closed source research. perhaps there will be some achievements privately, but all mind and matter is interco-mingled already and forever. secrets are just another way of saying "obscure path" ... feels?

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