# (Soft Question) Largest known semiprimes with no known factors

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?

• 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. – Eevee Trainer Dec 8 '18 at 22:27
• Maybe physics.open.ac.uk/~dbroadhu/cert/semgpch.gp is of interest. – gammatester Dec 8 '18 at 22:34
• 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. – Keith Backman Dec 9 '18 at 2:33
• @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. – Peter Dec 9 '18 at 14:11