3000 times a day? Doesn’t that just turn into repetitive prayer?
If one repeats anything, it is repetitive.
Perhaps you are alluding to Mt 6:7, “But when ye pray, use not vain repetitions, as
the heathen do.” Repeating the Lord’s name isn’t vain, especially when asking for his mercy.
At Mass we ask for the Lord’s mercy three times: Kyrie eleison, Christe eleison, Kyrie eleison. At Divine Liturgy, “Lord, have mercy” makes up for a majority of the responses (someone once told me 83% – whatever the percentage, it’s a lot).
From what I’ve read, the numbers mentioned in The Pilgrim’s Way are for monastic use and then only with the permission of your spiritual father.
Here’s the section on the Jesus Prayer in the Catechism, #2616, reminding us of the Biblical origins of it.
The urgent request of the blind men, “Have mercy on us, Son of David” or “Jesus, Son of David, have mercy on me!” has been renewed in the traditional prayer to Jesus known as the Jesus Prayer: “Lord Jesus Christ, Son of God, have mercy on me, a sinner!” Healing infirmities or forgiving sins, Jesus always responds to a prayer offered in faith: “Your faith has made you well; go in peace.”
You’ll also find it in the Luke 18: 9-14, in the Parable of the Pharisee and the Tax Collector where Jesus Christ speaks about it.
9He then addressed this parable to those who were convinced of their own righteousness and despised everyone else. 10“Two people went up to the temple area to pray; one was a Pharisee and the other was a tax collector. 11The Pharisee took up his position and spoke this prayer to himself, ‘O God, I thank you that I am not like the rest of humanity—greedy, dishonest, adulterous—or even like this tax collector. 12I fast twice a week, and I pay tithes on my whole income.’ 13But the tax collector stood off at a distance and would not even raise his eyes to heaven but beat his breast and prayed,
‘O God, be merciful to me a sinner.’ 14I tell you, the latter went home justified, not the former; for everyone who exalts himself will be humbled, and the one who humbles himself will be exalted.”