Sayyiduna Abdullah bin Umar (may Allah be pleased with them both) said that the Prophet (peace and blessings be upon him) would not leave these two corners, the Yamani Corner and the Black Stone, in any circuit; he would touch them both, and he would not touch the two that are next to the Hijr (the Hatim).
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 9259
Ubayd bin Umayr al-Laythi (may Allah have mercy on him) said: I asked Ibn Umar (may Allah be pleased with them both): "Why is it that I see you crowding at these two corners, and I have not seen anyone else among the Companions (may Allah be pleased with them) crowding at them besides you?" He said: "I heard the Messenger of Allah (peace and blessings be upon him) say: 'Touching them wipes away sins.'"
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 9260