Here
http://primes.utm.edu/glossary/xpage/Semiprime.html
I came across a number that baffles me! It has been proven(!) that the (constructed) number in the link is semiprime (the product of two primes) and, if I understand the link at the site correct, it is known that the smaller prime factor is greater than the third root of the number. But no factor of the number is known.
My questions :
Could the possibility to construct proven semiprimes with unknown factors mean, that deciding whether a given number is a semiprime is easier than integer factoriazation ?
I think this is not the case because even if a construction of the proof for a given random number is possible, it will not be feasible in practice, but perhaps I underestimate the power of the method.
In Wikipedia it is stated, that this method "might prove vulnerable to factorization" (See https://en.wikipedia.org/wiki/Semiprime)
Does that mean that the factors of the constructed number maybe can be calculated based on the method they are constructed, or that RSA might be unsafe because the method could find a curve constructing the public number ?