We know that the existence of good pseudorandom generators (PRGs) does not only imply $P=BPP$, but also $PromiseP=PromiseBPP$.
Let us assume $PromiseP\ne PromiseBPP$. Then good PRGs do not exist. However it is still possible that $P=BPP$ holds. If good PRGs do not exist then does $P=BPP$ imply $P=NP$ or is there a possibility $P\neq NP$ still might be true?
Is it possible to have $P=BPP$ without good PRGs and with $P\neq NP$ and with $PromiseP=PromiseBPP$?