Is it obligatory to re-perform past prayers that were missed due to a state of ritual impurity (janābah) from which one did not purify oneself by ghusl, given that the number of such prayers is not remembered, and considering that the initial state of janābah was due to ignorance of the obligation of ghusl?

The emission of semen necessitates ghusl (definition), based on the Prophet's (peace be upon him) saying: "And if you gush forth water, then perform ghusl." If you experienced a seminal emission and did not perform ghusl, then ghusl is obligatory upon you, and you must repeat all the prayers you performed while in a state of janabah (definition). If you do not know their number, then exert your best judgment and estimate what you believe will most likely clear your conscience. As for the days when you knew the obligation of performing a full-body ghusl and you performed it, then later doubted the completeness of the ghusl, you are not required to repeat the ghusl or the prayers, because the original assumption is the validity of the ghusl, and doubt after an act of worship does not have an effect.