Tirmidhi

English Commentary:
1:
It has been mentioned earlier (Hadith no. 439) that the Prophet (sallallahu alayhi wa sallam) did not perform more than eleven rak‘ahs of tahajjud (night prayer) in Ramadan or outside of Ramadan. In this hadith, however, there is mention of performing thirteen rak‘ahs. Some have counted the two sunnah rak‘ahs of ‘Isha within these thirteen, as sometimes he would delay them and combine them with the tahajjud prayer. Others have said that the two sunnah rak‘ahs of Fajr are included in this count, and there is mention of this in some narrations as well. Or it is possible that sometimes he performed eleven and at other times thirteen, and each narrator reported what he witnessed. However, there is no authentic narration of performing more than thirteen.

Hadith Commentary:
In this hadith, the number of rak‘ahs (units) of the Tahajjud prayer of the Messenger of Allah (sallallahu alayhi wa sallam) is mentioned, which were thirteen rak‘ahs. The Messenger of Allah (sallallahu alayhi wa sallam) would perform them in such a way that he would offer salutations (salam) after every two rak‘ahs.

In one narration of Sahih al-Bukhari, these rak‘ahs of the Messenger of Allah (sallallahu alayhi wa sallam) are reported as eleven.
(Sahih al-Bukhari, al-Tafsir, Hadith: 4569)
However, this narration is reported from Sharik ibn ‘Abdullah, who narrated this number from Kuraib, whereas other students of Kuraib report the number as thirteen rak‘ahs. On this basis, the narration of Sharik is considered less preferred (marjuh).

From ‘A’ishah (radi Allahu anha) as well, the number is reported as thirteen rak‘ahs, as there are multiple narrations regarding this in Sahih Muslim.

In any case, by including the initial two rak‘ahs at the time of Tahajjud prayer, their total number becomes thirteen.

For details, see the benefits of Hadith: 992.