It took me a while to understand your comment, until I realized there are
two interpretations of the question of where these numbers come from:
• One is a historical question: who first used these numbers and when? who copied from where?
• The other is a conceptual question: why might someone choose these numbers, what do they "mean", how do we interpret these constants?
The former is purely a question of facts and there is nothing to "explain the nature of the numbers", and this is what the answerer on Stack Exchange seems to have interpreted it as. Under this interpretation saying things like "the modulus is the period" is not really germane to the question; what's required is to search sources and try to find the chronologically earliest one. (The answer doesn't seem to have done a definitive job, but it's a reasonable start.)
This is like synchronic vs diachronic in linguistics: in the latter interpretation you mainly just want to understand the random-number generator.