Is the following statement consistent:

>``**There is no non-trivial c.c.c forcing notion adding a minimal generic real**''?

The question is related to Prikry's question:  Is it consistent that any non-trivial c.c.c forcing notion adds a Cohen real or a Random real?

See also [http://mathoverflow.net/questions/149316/a-special-c-c-c-forcing-notion-and-adding-minimal-generic-reals](http://mathoverflow.net/questions/149316/a-special-c-c-c-forcing-notion-and-adding-minimal-generic-reals) where it is shown that the answer to the above question is no, if we assume $CH$ or $MA+\neg CH$ (this follows from the results of Judah-Shelah in [Forcing Minimal Degree of Constructibility](http://projecteuclid.org/euclid.jsl/1183743725)) Also it is clear that, a model for Prikry's question is also a model for the above mentioned question.