All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ʻalayhi wa sallam, is His slave and Messenger.
It is well-known that, according to the majority of Muslim scholars, the sign of reaching puberty for a male is either of the following three: discharge of semen, growth of coarse pubic hair, or attaining 15 years of age based on the Hijri calendar. The Maalikis held the opinion that the male reaches puberty by attaining the age of 18; and the first is the preponderant view adopted in Islamweb. For more benefit, please refer to fatwa 83431.
As long as you are certain of the sign of growing coarse pubic hair at the age of 14, then this indicates that you reached puberty at that age, so you should make up for the prayers that you missed from that age. As for the prayers before attaining that age, you are not obliged to make up for them as long as you are not certain that you had reached puberty by then. The basic principle regarding that period (before 14) is that you had not reached puberty at that time unless you are certain that you had.
As for the number of prayers that you are obliged to make up for, if you are not certain about the number of prayers that you missed, then you are obliged to make up for a given number of prayers of which you believe that it is most likely enough to clear you from your liability. For instance, if you were uncertain of whether you missed ten or twenty prayers, then you make up for twenty out of precaution.
Shaykh Wahbah Az-Zuhayli wrote:
“Fifthly, making up for the missed prayers if the person does not know the exact number of the missed prayers: the Hanafis maintained that when the person is liable for making up for a number of prayers and the exact number is unknown to him, he is obliged to make up for a number of prayers until he feels that he most likely cleared himself from his liability ... The Maalikis, Shaafiʻis, and Hanbalis held that he is obliged to make up for a number of prayers until he believes with certainty that he cleared himself from his liability pertaining to the obligatory prayers...” [Al-Fiqh Al-Islaami]
Mahmood Khattaab As-Subki wrote:
“Benefit: when the person misses some prayers whose exact number is unknown to him, then he is obliged to make up for the missed prayers until he feels that he most likely cleared himself from his liability, according to the Hanafis and Maalikis, and until he believes with certainty that he cleared himself from his liability pertaining to those prayers, according to the Shaafi'is and Hanbalis.” [Ad-Deen Al-Khaalis]
There is no doubt that it is better to be on the safe side. For example, if you are unsure whether you missed the prayers of five or six months, then you should make up for the prayers of six months.
As for the prayers you performed while in a state of janaabah (major ritual impurity) out of ignorance of the obligation of ghusl, then you are obliged to make up for these prayers according to the view adopted by the majority of the Muslim jurists. Some scholars, though, held that you are not obliged to make up for them in this case.
Allaah Knows best.