How many Sahih(Authentic) Hadith are there?

From the size of the major Hadith collections, I'd estimate that there are only around 80 thousand at most, including overlapping Hadith. Some links (quite unreliable) seem to put the number closer to 10 thousand unique Sahih(Authentic) Hadith. Is there a study that identifies exactly how many are out there? If not, what are the major Sahih(Authentic) Hadith collections? To be precise, I'd like to know from a Sunni perspective. But answers from other sects would be interesting.