The prayer of glorification (Salat al-Tasbih)

It is narrated from Sayyiduna Ibn Abbas (may Allah be pleased with them both) that the Messenger of Allah (peace and blessings be upon him) said to Sayyiduna al-Abbas bin Abd al-Muttalib (may Allah be pleased with him): "O Abbas! O my uncle! Shall I not give you a gift? Shall I not give you a present? Shall I not do an excellent thing for you? There are ten qualities which, if you do them, Allah will forgive all your sins: the first and the last, the old and the new, the unintentional and the deliberate, the small and the great, the hidden and the open. You should pray four rak'ahs in this way: in every rak'ah recite Surah al-Fatihah and some other surah. When you have finished the recitation in the first rak'ah, then while still standing say 'Subhan Allah, wa al-hamdu lillah, wa la ilaha illa Allah, wa Allahu akbar' (Glory be to Allah, all praise is for Allah, there is no god but Allah, and Allah is the Greatest) fifteen times. Then bow and say it ten times while bowing; then raise your head from the bowing and say it ten times; then prostrate and say it ten times; then raise your head from the prostration and say it ten times; then make the second prostration and say it ten times; then raise your head from the prostration (before rising for the second rak'ah) and say it ten times. In this way it will total seventy-five times in each rak'ah; repeat the same in all four rak'ahs. If you can pray it once every day, then do so; if not, then once every Friday; if you cannot do even that, then once a month; if you cannot do even that, then once a year; and if you cannot do even that, then be sure to pray it once in your whole life."
Musa bin Abd al-Aziz narrated this hadith from al-Hakam bin Aban with a connected chain, and Abu Bakr bin Ishaq, Abu Dawud and al-Nasa'i recorded it, and all three of them narrated it from Abd al-Rahman bin Bishr.

(A narration reported in support of the previous hadith, with identical wording.) As for the condition of Musa bin Abd al-Aziz:

Abu al-Hasan Muhammad bin Muhammad bin Ya'qub narrated to me; Abdullah bin Muhammad bin Abd al-Aziz narrated to him; Muhammad bin Sahl bin Askar narrated to him; he said: I heard Abd al-Razzaq, when he was asked about Abu Shu'ayb al-Qinbari, and he praised him very highly. As for the scholarly standing of al-Hakam bin Aban:

Ahmad bin Muhammad bin Wasil al-Baykandi informed me; his father narrated to him; Muhammad bin Isma'il al-Bukhari narrated to him; Ali bin al-Madini narrated to him from Ibn Uyaynah, who said: I asked Yusuf bin Ya'qub: How was al-Hakam bin Aban (as a narrator)? He replied: He was our master (elder). As for Ibrahim bin al-Hakam bin Aban narrating this hadith from his father as mursal:

Ali bin Isa narrated to us; Ibrahim bin Abi Talib and Muhammad bin Ishaq narrated to him, both of them saying: Muhammad bin Rafi' narrated to us; Ibrahim bin al-Hakam bin Aban narrated to him; his father narrated to him; and Ikrimah narrated to him that the Messenger of Allah (peace and blessings be upon him) said to his uncle al-Abbas (may Allah be pleased with him) (then the narrator mentioned the whole hadith). Imam al-Hakim says: This narration being mursal does not weaken the hadith being connected (mawsul), because an addition in the chain (of the Companion's name) from a trustworthy narrator is more deserving and more acceptable than the mursal form. Moreover, the imam of hadith of that era, Ishaq bin Ibrahim al-Hanzali (Ibn Rahawayh), preserved this chain through Ibrahim bin al-Hakam bin Aban and narrated it as connected:

Abu Bakr bin Quraysh informed us; al-Hasan bin Sufyan informed him; Ishaq bin Ibrahim al-Hanzali informed him; Ibrahim bin al-Hakam bin Aban informed him from his father, he from Ikrimah, he from Ibn Abbas, and he from the Prophet (peace and blessings be upon him), like the hadith of Musa bin Abd al-Aziz from al-Hakam. And it is also authentically established from Sayyiduna Abdullah bin Umar bin al-Khattab (may Allah be pleased with them both) that the Messenger of Allah (peace and blessings be upon him) taught his cousin Ja'far bin Abi Talib (may Allah be pleased with him) this prayer (Salat al-Tasbih) just as he had taught it to his uncle al-Abbas (may Allah be pleased with him).

It is narrated from Sayyiduna Abdullah bin Umar (may Allah be pleased with them both) that the Messenger of Allah (peace and blessings be upon him) sent Sayyiduna Ja'far bin Abi Talib (may Allah be pleased with him) to the land of Abyssinia. When he returned, he (peace and blessings be upon him) embraced him and kissed him between his eyes, then said: "Shall I not give you a gift, shall I not give you glad tidings, shall I not present you with a present and a rare thing?" He said: Yes, O Messenger of Allah! He (peace and blessings be upon him) said: "Pray four rak'ahs, and in every rak'ah recite Surah al-Fatihah and some other surah. Then after the recitation, while still standing and before bowing, say fifteen times: 'Subhan Allah, wa al-hamdu lillah, wa la ilaha illa Allah, wa Allahu akbar, wa la hawla wa la quwwata illa billah' (Glory be to Allah, all praise is for Allah, there is no god but Allah, Allah is the Greatest, and there is no power and no strength except with Allah). Then bow and say it ten times; then raise your head from the bowing and say it ten times; then prostrate and say it ten times; then, before standing up (for the second rak'ah), say it ten times. In this way the first rak'ah will be complete. Then do the same in the remaining three rak'ahs until the four rak'ahs are complete."
This chain is sahih (authentic), with no ambiguity in it. One proof of the authenticity of this hadith is that from the era of the followers of the Successors (Atba' al-Tabi'in) up to our own time, the imams have acted upon it and have kept teaching it to people, among them Abdullah bin al-Mubarak.

Abu Wahb Muhammad bin Muzahim narrates: I asked Abdullah bin al-Mubarak about the prayer (Salat al-Tasbih) in which glorifications are recited. He said: Say the takbir, then say: 'Subhanaka Allahumma wa bi-hamdika, wa tabaraka ismuka, wa ta'ala jadduka, wa la ilaha ghayruka' (Glory be to You, O Allah, and with Your praise; blessed is Your Name, exalted is Your majesty, and there is no god besides You). Then say fifteen times: 'Subhan Allah, wa al-hamdu lillah, wa la ilaha illa Allah, wa Allahu akbar' (Glory be to Allah, all praise is for Allah, there is no god but Allah, and Allah is the Greatest). Then, after seeking refuge (ta'awwudh), recite Surah al-Fatihah and some other surah, then (before bowing) say these glorifications ten times; then ten times in the bowing; then ten times after raising the head from the bowing; then ten times in the prostration; then ten times after raising the head from the prostration (in the sitting); then ten times in the second prostration; and then ten times after raising the head from the prostration (while sitting). Pray four rak'ahs in this way, so there will be seventy-five glorifications in each rak'ah, and thus the total will come to three hundred. If you pray this prayer at night, then in my view it is better that you give the salam after every two rak'ahs; and if you pray it by day, it is up to you whether you give the salam or not.
All the narrators who narrate this hadith from Ibn al-Mubarak are trustworthy (thiqah) and reliable, and Abdullah bin al-Mubarak cannot be suspected of teaching something whose chain was not sahih in his view.