Indeed, We sent the Qur'an down during the Night of Decree. 97:1
And what can make you know what is the Night of Decree? 97:2
The Night of Decree is better than a thousand months. 97:3
According to Shi'a Islam, the Prophet (SAWW) did not specify the exact date of Laylatul-Qadr (night of decree), but there is a narration from the Prophet (s) which could be related with your question, so it has narrated that:
A person told Prophet Muhammad (SAWW) my house is far from Medina,, tell me the Laylatul-Qadr, the Prophet (SAWW) responded: come on 23th.
«وَ فِی رِوَایَةِ عَبْدِ اللَّهِ بْنِ بُکَیْرٍ عَنْ زُرَارَةَ عَنْ أَحَدِهِمَا(ع) قَالَ سَأَلْتُهُ عَنِ اللَّیَالِی الَّتِی یُسْتَحَبُّ فِیهَا الْغُسْلُ فِی شَهْرِ رَمَضَانَ فَقَالَ لَیْلَةُ تِسْعَ عَشْرَةَ وَ لَیْلَةُ إِحْدَى وَ عِشْرِینَ وَ لَیْلَةُ ثَلَاثٍ وَ عِشْرِینَ وَ قَالَ لَیْلَةُ ثَلَاثٍ وَ عِشْرِینَ هِیَ لَیْلَةُ الْجُهَنِیِّ وَ حَدِیثُهُ أَنَّهُ قَالَ لِرَسُولِ اللَّهِ ص إِنَّ مَنْزِلِی نَاءٍ عَنِ الْمَدِینَةِ فَمُرْنِی بِلَیْلَةٍ أَدْخُلُ فِیهَا فَأَمَرَهُ بِلَیْلَةِ ثَلَاثٍ وَ عِشْرِینَ»؛ من لا یحضره الفقیه، ج 2، ص 160 – 161.
(Man La Yahzarah al Faqih Vol.2, Pages 160-161)
In accordance with the majority of the Shia scholars view (according to some traditions), the night of decree or Laylatul-Qadr is probably one of the following days of Ramadan:
19th, 21st, 23rd .
Imam Aboo Ja’far Muhammad ebn Ali-al-Baqir (a.s.) is quoted in Bihar al-Anwar and Da’aim al-Islam as mentioned:
"The 17th night of the month of Ramadhan is when the 2 parties met,
and the 19th is at the time that the lists of the pilgrims is written down,
and the 21st is at the time that successors to the Prophets passed away and Jesus Christ (as) was raised to heaven and Moses (as) passed away,
whereas the 23rd is hoped to be Lailatul-Qadr."
No one knows about the exact date of laylatul Qadr because according to hadith, in last 5 days (that is 21st, 23rd, 25th, 27th and 29th) dates of Ramadan are generally called night of laylatul Qadr and we have to pray all the nights in these dates because Except Allah no one knows that which night is laylatul Qadr night but it is sure that in these five nights one night will be laylatul Qadr, That's why everyone prays on these nights.
Allah knows better