The "Skeptic's Prayer" is introduced on page 411 of Handbook of Catholic Apologetics: Reasoned Answers to Questions of Faith, by Peter Kreeft & Fr. Ronald Tacelli.
The Skeptic's Prayer
This claim---that all seekers find---is testable by experience, by experiment. If you are an honest scientist, here is a way to find out whether Christianity is true or not. Perform the relevant experiment. To test the hypothesis that someone is behind the door, knock. To test the Christian hypothesis that Christ is behind the door, knock.
How do you knock? Pray! Tell Christ you are seeking the truth---seeking him, if he is the truth. Ask him to fulfill his promise that all who seek him will find him. In his own time, of course. He promised that you would find, but he didn't promise a schedule. He's a lover, not a train.
But---you may reply---I don't know whether Christ is God. I don't even know whether there is a God. That's all right; you can pray the prayer of the skeptic:
God, I don't know whether you even exist. I'm a skeptic. I doubt. I think you may be only a myth. But I'm not certain (at least when I'm completely honest with myself). So, if you do exist, and if you really did promise to reward all seekers, you must be hearing me now. So I hereby declare myself a seeker, a seeker of the truth, whatever it is and wherever it is. I want to know the truth and live the truth. If you are the truth, please help me.
If Christianity is true, He will. Such a prayer constitutes a scientifically fair test of the Christian "hypothesis"---that is, if you do not put unfair restrictions on God, like demanding a miracle (your way, not his) or certainty by tomorrow (your time, not his). The demand that God act like your servant is hardly a scientifically fair test of the hypothesis that there is a God who is your King.
But all this King asks for at first is honesty, not faking a faith you do not have. Honesty is a choice of the will---the choice to seek the truth no matter what or where. This is the most momentous choice you can make. It is the choice of light over darkness, ultimately heaven over hell.
Honesty is infinitely more momentous than we often think. It is also much harder than we think. Our culture trivializes honesty into merely "sharing your feelings", telling others about the state of our nerve ends. That's not the opposite of dishonesty, that's just the opposite of shame or shyness. Shallow honesty seeks "sharing"; deep honesty seeks truth. Shallow honesty stands in the presence of others; deep honesty stands in the presence of God.
The authors assert that this constitutes a "scientifically fair test of the Christian 'hypothesis'".
Can the "Skeptic's Prayer" really be considered a valid scientific experiment?
Notes
Interestingly, the attempt to portray this prayer in a 'scientific' light brings to mind John Lennox's assertion that Christianity can be tested (see Is Christianity testable?).
The notions of 'knocking on the door' and 'all seekers find' were probably taken from Jeremiah 29:13, Matthew 7:7-11, and Luke 11:5-13:
13 You will seek me and find me, when you seek me with all your heart. (Jeremiah 29:13 ESV)
7 “Ask, and it will be given to you; seek, and you will find; knock, and it will be opened to you. 8 For everyone who asks receives, and the one who seeks finds, and to the one who knocks it will be opened. 9 Or which one of you, if his son asks him for bread, will give him a stone? 10 Or if he asks for a fish, will give him a serpent? 11 If you then, who are evil, know how to give good gifts to your children, how much more will your Father who is in heaven give good things to those who ask him! (Matthew 7:7-11 ESV)
5 And he said to them, “Which of you who has a friend will go to him at midnight and say to him, ‘Friend, lend me three loaves, 6 for a friend of mine has arrived on a journey, and I have nothing to set before him’; 7 and he will answer from within, ‘Do not bother me; the door is now shut, and my children are with me in bed. I cannot get up and give you anything’? 8 I tell you, though he will not get up and give him anything because he is his friend, yet because of his impudence he will rise and give him whatever he needs. 9 And I tell you, ask, and it will be given to you; seek, and you will find; knock, and it will be opened to you. 10 For everyone who asks receives, and the one who seeks finds, and to the one who knocks it will be opened. 11 What father among you, if his son asks for a fish, will instead of a fish give him a serpent; 12 or if he asks for an egg, will give him a scorpion? 13 If you then, who are evil, know how to give good gifts to your children, how much more will the heavenly Father give the Holy Spirit to those who ask him!” (Luke 11:5-13 ESV)