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Is there a list, similar to prime numbers and probable primes, of the largest semiprimes with unknown factors? Is there a list of numbers that are either semiprime or prime, with no known factors? Is there literature on how to find large semi primes?

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  • $\begingroup$ I feel like a list of "possible semiprimes" would likely be at least somewhat coincident with a list of possible primes, given that a large semiprime accordingly has large prime factors (so finding said factors would be difficult, thus rendering the number a possible candidate for either). As for finding large semiprimes, I feel the easiest method would just be to multiply two large known primes together, but I imagine you want something more elegant. $\endgroup$ – Eevee Trainer Dec 8 '18 at 22:27
  • $\begingroup$ Maybe physics.open.ac.uk/~dbroadhu/cert/semgpch.gp is of interest. $\endgroup$ – gammatester Dec 8 '18 at 22:34
  • $\begingroup$ It's unclear how one could be certain that a large number was a semiprime (as opposed to having three or more prime factors) without knowing the two prime factors which multiply to it. $\endgroup$ – Keith Backman Dec 9 '18 at 2:33
  • $\begingroup$ @KeithBackman Surprisingly, this seems to be possible. I heard from a construction of a number which could be proven to be semiprime without known factors (according to the claim, not even by the constructor himself). For huge number, this method is probably not feasible. $\endgroup$ – Peter Dec 9 '18 at 14:11
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It doesn't exist. Any area of rectangle which sides are prime is a semiprime.

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    $\begingroup$ There are also infinite many primes, but nevertheless it makes sense to speak of the largest known prime. $\endgroup$ – Peter Dec 9 '18 at 14:13

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