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by ColinWright 4052 days ago
When you use factoring algorithms other than simple trial division - things like Pollard rho and its ilk - you are not guaranteed to get the smallest factor(s) first. Sometimes you get bigger factors, or combinations of factors, because those are what happen to pop out of the algebraic structure you're running over.

But any "primes" being used should have some serious factorisation algorithms run over them before being used, so this is really embarrassing.

EDIT

And to answer contravariant's question[0]:

    Also, shouldn't it only
    have 2 prime factors?
It's possible that one of the "primes" it found was in fact composite, and it's that "prime" that has these factors. So you generate two large primes and multiply them together, not realising that one of your "primes" wasn't.

[0] https://news.ycombinator.com/item?id=9561051

1 comments

Large pseudo prime generators usually check for divisibility by numbers upto a million or so, then follow it with Rabin-Miller or more sophisticated non-deterministic tests to verify primes.

These primes could not have been generated by any reputable prime generation algos that I can imagine.