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1 Thessalonians 5:17 gives the answer.
"Rejoice at all times. Pray without ceasing. Give thanks in every circumstance, for this is God’s will for you in Christ Jesus." (Berean Study Bible)
You are enjoined to pray without ceasing.
Q: Does this mean I should be constantly repeating words of prayer, either out loud or subvocally?
A: No, that is not what is meant. It means one ought to be continually seeking out and communing with God in one's heart. This is the essence of prayer, and one is enjoined to cultivate that attitude of the heart without ceasing.
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Although we are encouraged to pray frequently, even "without ceasing" (1 Thessalonians 5:17) as noted in another answer, a requirement to pray would be a form of works righteousness, which is explicitly condemned, especially by Paul (e.g. Ephesians 2:8-9).
As far as I know, no Protestant/Reformed denominations require prayer.
That said, Catholics reject Sola Gratia and impose various requirements on parishioners as "penance", which I believe may include saying prayers, though as I understand this usually takes the form of "you did X; as penance, say the Lord's Prayer Y times" and not a requirement to pray a specific number of times per day.
I don't know about Orthodox...
Upvote:2
There is no common rule to Christians. Most monastic traditions know frequent fixed prayer times. They are not fixed by any OT or NT scripture but on the rules of the order or the monastery or convent. Commonly, there are the Laudes in the morning, several hour prayers during the daytime, the Vesper in the evening and the Complet in the night.
Protestants usually pray before the meals (morning, lunch, dinner) and in the sunday service. They may pray at any time they want. There is no fixed obligation for prayer for laic Christians.