The chief of the verses of the Quran is Ayat al-Kursi

It is narrated from Sayyiduna Abu Hurayrah (may Allah be pleased with him) that the Messenger of Allah (peace and blessings be upon him) said: "The chief of all the verses of the Qur'an is Ayat al-Kursi."
This hadith has a sahih (authentic) chain, but the two Shaykhs (Bukhari and Muslim) did not record it.

It is narrated from Sayyiduna Nu'man bin Bashir (may Allah be pleased with him) that the Prophet (peace and blessings be upon him) said: "Indeed, Allah Almighty wrote a Book two thousand years before creating the heavens and the earth, and from it He revealed two verses with which He concluded Surah al-Baqarah. In whatever house these verses are recited, the devil does not come near it for three nights."
This hadith is sahih (authentic) on the condition of Muslim, but the two Shaykhs (Bukhari and Muslim) did not record it.

It is narrated from Sayyiduna Abdullah bin Mas'ud (may Allah be pleased with him) concerning the sayings of Allah Almighty: "Alif Lam Mim. That is the Book" [Surah al-Baqarah: 1-2], that he said: "Alif Lam Mim" is a letter of the name of Allah, and "the Book" means the Qur'an, while "There is no doubt in it" means that there is no room for any kind of doubt or suspicion in it (the Divine Word).
This hadith is sahih (authentic) on the condition of Muslim, but the two Shaykhs (Imam Bukhari and Muslim) did not record it.

The Companions of the Messenger of Allah (peace and blessings be upon him) and their faith were mentioned in the presence of Sayyiduna Abdullah bin Mas'ud (may Allah be pleased with him), and he said: "The matter of Muhammad (peace and blessings be upon him) was perfectly clear to those who saw him (peace and blessings be upon him) with their own eyes. But by the One besides whom there is no true deity, no believer's faith is superior to faith in the unseen." Then he recited these verses, from "Alif Lam Mim. That is the Book about which there is no doubt" up to "who believe in the unseen" [Surah al-Baqarah: 1-3].
This hadith is sahih (authentic) on the condition of the two Shaykhs (Imam Bukhari and Muslim), but they did not record it.

It is narrated from Sayyiduna Abdullah bin Mas'ud (may Allah be pleased with him) that the stones which Allah Almighty mentioned in the Qur'an, "whose fuel is people and stones" [Surah al-Baqarah: 24], are stones of sulphur which Allah Almighty created with Him however He willed, or as He willed.
This hadith is sahih (authentic) on the condition of the two Shaykhs (Bukhari and Muslim), but they did not record it.

It is narrated from Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) that Allah Almighty had expelled Sayyiduna Adam (peace be upon him) from Paradise before anyone (else of mankind) had entered it. Allah Almighty said: "Indeed, I will place upon the earth a successor." They said: "Will You place upon it one who causes corruption therein and sheds blood?" [Surah al-Baqarah: 30] For two thousand years before his creation, the jinn, that is, Banu al-Jann, had been on the earth, and they caused corruption on the earth and shed blood. So when Allah Almighty said: "Indeed, I will place upon the earth a successor," the angels, in view of the deeds of the jinn, that is, Banu al-Jann, said: "Will You place upon it one who causes corruption therein and sheds blood?" meaning: Will You create in it a creation that will spread corruption and shed blood? For when those jinn had caused corruption on the earth, Allah sent against them an army of angels, who struck them and drove them away to the islands of the seas. So the angels said: "Will You place upon it one who causes corruption therein?" meaning: Will You make in it one who will cause corruption just as those Banu al-Jann did? Then Allah said: "Indeed, I know what you do not know."
This hadith has a sahih (authentic) chain, but the two Shaykhs (Bukhari and Muslim) did not record it.

It is narrated from Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) that when Allah Almighty had finished creating Sayyiduna Adam (peace be upon him) and the soul began to flow through him, he sneezed and said: "Al-hamdu lillah (All praise is for Allah)." His Lord said to him: "May your Lord have mercy on you."
This hadith has a sahih (authentic) chain, but the two Shaykhs (Bukhari and Muslim) did not record it. Attab has narrated it with a connected chain via Khusayf, but that is not on the condition of this book.