What is the ruling on the prayers of one who masturbated but did not perform ghusl, and it is not mentioned whether he knew at the time the obligation of ghusl due to the emission of semen, knowing that about a month and a half has passed since then?

You must make up for the prayers you performed without performing ghusl after the emission of semen, because purification is a condition for the validity of prayer. This is the view of the majority of scholars. Your inability to recall whether you knew or were ignorant of the obligation of ghusl does not affect the obligation to make up the prayers, according to the majority of scholars. You must also repent from masturbation.