It is certain that Night of Qadr is the month of Ramadan as per the holy Qur'an, but the Qur'an does not reveal the exact Night of Qadr. However, in the sayings of the Prophet and his household (P) more emphasis is given to the 23rd of Ramadan.
First of all, it must be noted that according to the glorious Qur'an the Night of Qadr is in the month of Ramadan. Because, Allah (SWT) confirms that the Qur'an is revealed to the Prophet (P) in this month [2:185] saying that “We have indeed revealed this (Quran) in the Night of Qadr.” [97:1] based on these two verses of the Qur'an, it becomes clear that the Night of Qadr is certainly in this month. However, the holy Quran has not clarified that which night of Ramadan is the exact Night of Qadr. Referring to the sayings of the Prophet (P) and Ahl-Albait (A) we find that it is very much likely that the Night of Qadr is one the following nights: the 19th, 21st, or 23rd night of Ramadan. To be more precise, it could be mentioned that the strongest emphasis is laid on the 21st and the 23rd, particularly the 23rd. [1]
[1] See: Behar al-Anwar, v94, p4; Mustadrak al-Wasa'el, v7, p474.