I was wearing socks believing that they covered all my feet. I was surprised, after finishing prayer, to find that there was a hole in my sock the size of a fingerprint. My question is, were those prayers valid? Should I make up for them?
May Allaah reward you.

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 ‘alayhi wa sallam, is His Slave and Messenger.

If this hole was above the ankle, then there is no harm done; for it is not on the area that should be washed during ablution. However, if this hole was on the ankle or below it, then it is within the area of ablution. Jurists’ held different opinions on whether or not to wipe over the socks in this case.

Imaam Ahmad’s school of Fiqh ruled that it is impermissible as they would not cover the whole foot, and this is one of the opinions of Imaam Ash-Shafi‘i as well. This is because what is uncovered should be washed and what is covered should be wiped over, and if these two events combine, then washing takes precedence as if the feet became fully uncovered.

Abu Haneefah’s school of Fiqh ruled that if the tear reaches the size of three fingers, then it is impermissible to wipe over them during ablution, and if it were less than that, it is permissible.

Imaam Maalik’s school of Fiqh ruled that if the hole is the third of the size of the socks, then it is impermissible to wipe over them during ablution, and if it were less than that, it is permissible.

The scholars who adopted this opinion relied on the generality of the narrations on wiping over the leather socks; they did not specify that leather socks should be free from any kind of tears or holes. As long as one can walk with the leather socks, then they are just like the good ones. Besides most of the late Arabs’ leather socks were torn, and the Prophet, sallallaahu ‘alayhi wa sallam, commanded the Companions to wipe over them without giving any details. Thus, the ruling is applied to the people’s commonly worn leather socks at that time, most of which were torn. Additionally, if these leather socks were prohibited for one in the state of Ihraam to wear them, and wearing them entails expiation, then it is permissible to wipe over them in ablution just like those that are free of tears.

Hence, it is permissible to wipe over torn leather socks as long as the tears are small, based on the previously-mentioned evidence.

Socks take the same ruling as leather socks; accordingly, this tear, which is the size of a fingerprint, is considered a small tear and it is permissible to wipe over the socks. Therefore, your ablution was valid and you do not have to make up for those prayers.

Allaah Knows best.