What is the sunnah side to sleep on?

What side did Our Prophet Muhammad (pbuh) use to sleep on?

The sunnah way of sleeping is sleeping on right side

As narrated in the hadiths below, Prophet Muhammad (pbuh) used to sleep on his right side putting his right hand on his right cheek.
Narrated Al-Bara ibn Azib (ra),
"When the Messenger of Allah (pbuh) used to retire to his bed, he would lie on his right side and then say, 'O Allah, I surrender my soul to You and I turn my face to You and I entrust my affair to You and I seek Your support with hope and fear of You. There is no refuge from You but to You. I have believed in Your Book which You sent down and Your Prophet whom You sent.'" (Bukhari)
Hudhayfah (ra) said,
“When the Prophet (pbuh) went to bed at night, he would put his hand under his cheek, then say, ‘Allaahumma bismika amootu wa ahyaa (O Allaah, in Your name I die and I live).’ Then when he woke up he would say, ‘Al-hamdu Lillaah alladhi ahyaanaa ba’da ma amaatanaa wa ilayhi al-nushoor (Praise be to Allaah who has brought us back to life after causing us to die, and to Him is the resurrection).’” (Bukhaari)

Our Prophet (pbuh) recommended us to sleep on right side and take wudu before going to bed

al-Bara' ibn 'Azib reported:
“The Prophet (pbuh) said to me; 'Whenever you go to bed, do wudu as you do wudu for the prayer and then lie down on your right side. Then say...'" and he mentioned the rest of it and in it is, "Make that the last of the words that you utter." [Bukhari, al-Wudu)

Lying on stomach is the position Allah (swt) hates

Ya'ish ibn Tikhfa al-Ghifari said,
"My father said, 'Once while I was lying on my stomach in the mosque, a man moved me with his foot and said, "This is a position which Allah hates."'" He said, "I looked up and it was the Messenger of Allah, may Allah bless him and grant him peace." [Abu Dawud]

The Blessed Prophet (pbuh) used to lie on his back while having a short-lasting rest

'Abdullah ibn Zayd reported that he saw the Messenger of Allah, may Allah bless him and grant him peace, lying on his back in the mosque with one foot on top of the other." [Agreed upon]

Science approves that Prophet Muhammad (pbuh) is a great example to follow

Prophet Muhammad’s sleeping posture is exactly the same what today’s science recommends:
Science tells us that the best sleeping posture is lying on right and lying on back. It helps us relax and provides our internal organs, especially our heart, a proper rest. However, it says that sleeping on left causes lungs, stomach and liver to press against heart and prevents a resting sleep.
Sleeping on stomach causes pressure on all internal organs especially heart. It also results shallow breathing which avoids having a rest and causes waking up tired. It causes neck and back problems, as well.
It is extremely marvellous to see that Prophet Muhammad (pbuh), nearly 14 centuries ago, performed and recommended the best way which science has recently discovered. It is a clue that he is a righteous Prophet who had his knowledge through the revelation of Allah (swt).