The request of the prayer is intriguing, in essence "Please God, forget our sins." It's a biblical concept. In fact, under the New Covenant (Testament), God promises those who live faithful Christian lives that He will forget their sins. "For I will be merciful to their unrighteousness, and their sins and their lawless deeds I will remember no more" (Heb. 8:12).
Obviously, God is not forgetful, at least not in the sense that human beings experience forgetfulness. Yet God promises to forget (forgive) the sins of those who turn to Him in repentance and properly seek His forgiveness. It's not that it slips God's mind but rather that He chooses to forget our sins. When God forgives one who properly seeks His forgiveness, it's as if the sin never happened. The slate is totally clean, so to speak. There is no more record of the sin in God's mind. It has been, in an absolute sense, forgiven (forgotten)!
That's God's mercy and grace! The point at which God chooses to forget a person's sins is clear. It is when that person repents of his sins and seeks God's forgiveness through baptism into Christ. Ananias asked Saul, "And now why are you waiting? Arise and be baptized, and wash away your sins..." (Acts 22:16).
Are you carrying around with you a burden of sin? Wouldn't you like for God to forget your sins? The opportunity is just as real for you as it is for everyone else. If you will repent of your sins and surrender to your Savior in baptism, the blood that He shed on the cross long ago will still cleanse you of your guilt. As you are baptized into Christ, God will forget (forgive) your former iniquities. What a blessing! What are you waiting for?