This has been studied. There is no reason to believe that prayer has effects distinguishable from random chance or a placebo effect. Funnily enough telling sick people that they were prayed for made them slightly worse (reason is a bit unclear, possibly because this made them more worried, increasing stress.)
Your "studies" are not universal fact. It is illogical to base a sweeping opinion on a study which cannot account for billions who pray(ed) with results not necessarily known throughout history.
Furthermore you don't need to prove that something isn't real, you have to prove that something is real.
are the one attacking the merit/effect of prayer, thus the burden of proof (that it does not work) is yours, otherwise, you are simply posting in the negative for the sake of atheist agenda, which does not walk hand in hand with truth about prayer, or anything else.