I am looking for some of the ahadiths quoted by Mustadrak al-Hakim and are found in both muslim and bukhari or in one of them.
Among these ahadith which are quoted in either one or both sahihsyou may find:
In the book of Adab (in al-Mustadrak and in sahih al-Bukhari):
- The Prophet (ﷺ) said, "The most awful (meanest) name in Allah's sight." Sufyan said more than once, "The most awful (meanest) name in Allah's sight is (that of) a man calling himself king of kings." Sufyan said, "Somebody else (i.e. other than Abu Az-Zinad, a sub-narrator) says: What is meant by 'The king of kings' is 'Shahan Shah.,"
(sahih al-Bukhari and in al-Mustadrak -only in Arabic-)
And in the book of Riqaaq -To make the Heart Tender- (in both al-Mustadrak and sahhih al-Bukhari) you may find:
In the book of Dua' (in al-Mustadrak) and the book of Riqaaq (sahih Muslim) you may find:
Note that here the narrator chain are not that identic as al-Hakim narrates via ibn Wahb (student of imam Malik and al-Laith ibn Sa'ad) in a longer chain and a slight difference in the wording.
Sources: the book of Imam ad-Dhahabi called talkiss al-Mustadrak التلخيص (Summary of al-Mustadrak) and a thesis on the sahih qualification of al-Hakim and ad-Dhahabi called تصحيح أحاديث المستدرك بين الحاكم النيسابوري والحافظ الذهبي