Ibn'Umar (Allah be pleased with them) reported that when Messenger of Allah ﷺ circumambulated in Hajj and Umra he walked swiftly in the first three circuit about the House, and then walked in four circuits, and then observed two rak'ahs of prayer, and then ran between al-Safa and al-Marwa. (Using translation from Muslim 1261b)  

أَنَّ رَسُولَ اللهِ ﷺ كَانَ «إِذَا طَافَ فِي الْحَجِّ وَالْعُمْرَةِ أَوَّلَ مَا يَقْدَمُ فَإِنَّهُ يَسْعَى ثَلَاثَةَ أَطْوَافٍ وَيَمْشِي أَرْبَعًا ثُمَّ يُصَلِّي سَجْدَتَيْنِ ثُمَّ يَطُوفُ بَيْنَ الصَّفَا وَالْمَرْوَةِ»  

"When the Messenger of Allah came to Makkah he entered the Masjid and touched the Stone, then he moved to his right and walked rapidly for three (rounds) and then walked (at a regular pace) for four. Then he came to the Maqam and said: 'And take you (people) the Maqam (place) of Ibrahim as a place of prayer and prayed two Rakahs with the Maqam between him and the House. Then he came to the Hosue after praying those two Rakahs and touched the Stone, then he went out to As-Safa." (Sahih) Chpater 150. In How Many Rounds Should Be Quick? (Using translation from Nasāʾī 2939)  

لَمَّا قَدِمَ رَسُولُ اللهِ ﷺ مَكَّةَ دَخَلَ الْمَسْجِدَ فَاسْتَلَمَ الْحَجَرَ ثُمَّ مَضَى عَلَى يَمِينِهِ فَرَمَلَ ثَلَاثًا وَمَشَى أَرْبَعًا ثُمَّ أَتَى الْمَقَامَ فَقَالَ {وَاتَّخِذُوا مِنْ مَقَامِ إِبْرَاهِيمَ مُصَلًّى} [البقرة 125] فَصَلَّى رَكْعَتَيْنِ وَالْمَقَامُ بَيْنَهُ وَبَيْنَ الْبَيْتِ ثُمَّ أَتَى الْبَيْتَ بَعْدَ الرَّكْعَتَيْنِ فَاسْتَلَمَ الْحَجَرَ ثُمَّ خَرَجَ إِلَى الصَّفَا