I’ve been developing this simple proof for some time.
Even thought it is very difficult if not impossible to prove a negative, it is easier if the claim itself can be proven false. For instance, if I claim my wife has a blue Toyota and the DMV says there is no record of a blue Toyota owned by my wife, its proof that she does not, at least legally, own a blue Toyota, proving my claim is false.
My argument that God of the Bible does not exist comes from the claims of the Bible itself, though the many verses which espouses that prayer will work. But the argument doesn’t stem from the lack of prayers being answered as you might guess.
If we look at all the religions that have a god or gods, nearly all of them claim their god answers prayers yes, no or maybe. To put this more simply, if we take a person on their death bed and ask them how many prayers God has answered yes no or maybe during their lifetime, we immediately have to exclude all the ‘maybes’ because this person is about to die. The only prayer that might be a ‘maybe’ is if they are going to heaven, although technically that prayer would not be answered when the person is still alive.