For those that believe, God's purpose for us is to worship him and he tests which of us are good in this, he can reward/punish in this life or the next. Prayers are an act of worship and in Islam we believe its the first thing to be judged, there is only One God, the God of Adam, Noah, Moses, Jesus, Muhammad.
Righteous is just believing in the One God and being good (you've seen the Law in the Torah and the essence of these not to steal, murder, adultery, etc continues into the New Testament) and the Qur'an is a reminder of what God has said before with a few corrections. Prayer is a good deed to wipe out small sins.
Q11:114 "And perform prayer...surely good deeds remove the evil deeds"
Q2:153 "Seek help in patience and prayer"
Q23:1-2 "Successful indeed are the believers, who are humble in their prayers"
In Islam we bow our Heart and Mind to God in humble subservience (at least 17 times a day in the 5 prayers), as did Jesus - just the one time it says in the current Bible on the day of the last super, but he did go away for evening prayer and again for night prayer (Maghrib and Isak, maybe? - but we believe we all born Muslim anyway)
Q13:28 "Without doubt, in the remembrance of God do hearts find satisfaction"
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