What is the ruling concerning the prayers I performed while reciting the Qur’an to myself without moving my lips, knowing that this was due to ignorance?

Prayer is not valid unless the tongue and lips are moved and the letters are pronounced from their proper articulation points. Scholars differed whether it is a condition for oneself to hear (the view of the majority) or if merely pronouncing the letters is sufficient (the view of the Malikis and the choice of Ibn Taymiyyah). Whoever prayed in a manner that is not valid, must repeat those prayers because they are a debt upon him, and he must hasten to make them up, along with repentance and seeking forgiveness for his negligence in learning the rulings.