On mouth Athos they are saying the shorter form of the Jesus Prayer:
Lord Jesus Christ, have mercy on me
Here is a post from a monk from month Athos, who was active and posted on r/OrthodoxChristianity:
There was a thread few days ago about praying with Jesus' prayer for someone else and there were a lot of good answers which, perhaps, need some more clarifications and small changes which was difficult to do there, on place, because of many reasons. Hence, because I think that it is a theme of general interest, I will try to clarify it here.
Jesus' prayer (“Lord Jesus Christ have mercy on me”) is regarded by many and from a long time the most powerful prayer (reasons in the link provided).
As you know it isn't about a magical formula but a formula which meets certain factors/requirements which allow it to reach its maximum of efficiency. Let us concentrate on its 'purity' - that is without thoughts.
This purity stems from the fact that it is very short, without any other meanings, hence the mind isn't distracted. There are another variations which are contained in the most expanded "Lord Jesus Christ, Son of God, have mercy on me, the sinner for the prayers of Mother of God and all your saints. Amen." however, the experience in Mount Athos (and not only) shown that so many words and meanings distract our mind from the core of prayer and from guarding our heart – because we should never forget what the prayer is – and from enough time, the Athonite tradition (and not only) has the formula as “Lord Jesus Christ have mercy on me”. This is especially true nowadays when our mind is so wounded because of our distorted way of learn and live.
Another important factor which will keep our mind in prayer is the prayer rope which helps us in various ways to attain this purpose.
Also, it helps to whisper the prayer, if the environment permits.
Of course that we can pray for someone else (sometimes this can trigger a demonic attack tough), by using the Jesus' prayer or not, but based on the above rationale, in the Mount Athos the way of praying is the following one which proved the best one during the ages: At the first knot of the prayer rope we say "Lord Jesus Christ have mercy on your servant [name]" and at all the other knots we say "Lord Jesus Christ have mercy on your servant". We do not say the name of the one for which we pray because can be a big source of wandering and we want to avoid the wandering of the mind and any kind of thoughts at any cost.
Sometimes one can simply pray with “Lord Jesus Christ have mercy on me” knowing that God knows that in "have mercy on me" is included also his neighbor. This is the best way for someone which is at the beginning of the spiritual life.
I hope that this will clarify a little the matter of the efficiency of Jesus' prayer for someone else or for ourselves.
Like someone else said, by adding "the/a sinner" we shift away our focus from Christ to us and we are in danger to transform the prayer into a speak with ourselves. It is a source of mind wandering (in fact the main topic of my OP). The "a sinner" is not needed because is already contained in "have mercy on me" - it gives us enough humbleness.
--- Another aside is that one of the diseases of the century is a very dark and dangerous pack of depression / lack of courage / lack of true faith / lack of strong & healthy nervous system / constant sorrows / lack of conscience that we have eternal life etc. You cannot press such people too much to feel "sinners" because the will not bear it. I remember St. Paisios and St. Porfyrios (especially St. Paisios, of course) saying a lot of jokes. And I mean A LOT of jokes. We cannot accuse them of lack of discrimination, isn't it?
In Acts when John and Peter come out of the temple and they speak to the lame man saying:
"Silver and gold I do not have, but what I do have I give you: In the name of Jesus Christ of Nazareth, rise up and walk."
When I read this I gained some understanding of the Jesus Prayer. As Peter later says:
"There is no other name under heaven given among men by which we must be saved."
If Peter and John had all the gold and silver in the world, it would not have given the lame man what he truly desired. Instead they gave him the name of our Lord, and this was all he really needed. The name Lord Jesus Christ is the most precious thing we possess, and this is the power of the Jesus Prayer.
For this reason when we say it we should say it like we are carrying the most precious treasure.
@xmdr Thank you for replying and linking that thread. Although everything is worth a good reflection, at a first glance I liked very much the approach of not adding the "a sinner" as a way of humbling ourselves and keeping our focus on God.
@Lawrence87 Thank you very much for this little meditation.
@SimpleMan Thank you! I will watch the video tonight. I can relate to that last sentence. It’s annoying, but whatever takes us to God is a good thing in our lives. The problem is how stubborn we can be turning our backs to God. Sigh…