Is it obligatory for someone who has prayed for a long period, ignorant of a pillar of prayer or ritual purity, to repeat those prayers?

Purity (taharah) is a condition for the validity of prayer (salat). If the ablution (wudu) is not valid—for example, if a person did not wash their hands or did not wipe their head—then their prayer performed with this ablution is not valid, and they must repeat it.