Is the Jesus prayer one for the whole world? - Saint Sophrony

How Saint Sophrony learned about the Jesus Prayer

I remember a wonderful moment that is forever imprinted in my mind. It was at the very beginning of my monastic life, in 1925 or 1926. I was walking on the seashore, and there I saw an old man with a long prayer rope of 300 knots. I approached him with the fear of a beginner and I stood silently, watching him pray. And he was sitting on a large stone, moving from knot to knot [with his thumb]. 

Is the Jesus Prayer a prayer for the whole world?

 I dared to ask him, “Father, pray for me!” I asked for it because when I left France in 1925, I was overwhelmed by the spirit of “despair,” although in a less heavy form than now. And so, crushed by that despair, I asked him, “Father, pray for me!” He looked at me and said, “Do you see this prayer rope? I say it for the whole world. I pray for the whole world. And you are there, in my prayer.” It is hard to explain why, and how much time we need for a certain reaction, yet I did not leave after the first word. And after a while, living in myself the despair of those days, I said to him again: “Father, pray for me!” He says, “I have already told you that I am praying for the whole world. And you are here, in this prayer.” After a few moments, I repeated my request again, because my grief was deep, and again, the third time, I said timidly, “Father, pray for me!” 

He was told again and again, it's a prayer for the whole world.

He looked at me kindly and said, “But I told you that you are here,” pointing to the prayer rope,  “what do you need more? You are here in this prayer of mine for the whole world.” I departed, struck by the state of mind of this elder. “I pray for the whole world; you are there so that we do not ‘split’ into pieces for insignificant things.” 

On Mount Athos further questions about what this means

Having just reached Athos, and encountering such a form of prayer, of course I was impressed. I kept thinking, “What does this elder think when he prays for the whole world — does he think in time, in space, about the whole mankind from Adam to the present day? Or was his thought even deeper and more comprehensive?

Link to Audio recording- https://otelders.org/theology-and-spirituality/the-power-of-jesus-prayer-saint-sophrony-july-11-meeting-a-hermit-on-the-seashore/