It is truly sad and indeed unfortunate that we have no writings from Jesus.  If prayer has 'concrete' effects, any, forget the impossible to comprehend 'infinite effects;  what are they, and show the evidence.  NONE as you claim are scientifically confirmed, though many have claimed to be.  "healings incongruent with the known course of disease, etc."  are not scientifically confirmed healings.  In fact, quite opposite;  they are a confirmation of 'ignorance'.  Throughout history the legacy has been to affirm to a god what was not known at the time.  That is the 'god of the gaps' argument.  But, 'was once not known'  at a particular time has been filled later by discovery.  Unknown causes of healing now will be known and understood in a later tomorrow.  'No known medical rationale for healing, is not a miracle, it is a statement of ignorance.