How many "puranas" are there?
Are there any authentic full list of all the puranas (not just 18 mahapuranas) backed by some other puranas or scriptures?
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For the Puranas and Upapuranas- we get their names in the Devi Bhagavata Purana. There are 18 Puranas and 18 Upapuranas.
1-11. Sûta said :-- “O best of the Munis! I am now telling you the names of the Purânas, etc., exactly as 1 have heard from Veda Vyâsa, the son of Satyavati; listen. The Purâna beginning with "ma" are two in number; those beginning with “bha” are two; those beginning with “bra" are three; those beginning with "va” are four; those beginning respectively with “A”, “na”, “pa”, “Ling”, “ga”, “kû” and “Ska” are one each and “ma” means Matsya Purâna, Mârkandeya Purâna; “Bha” signifies Bhavisya, Bhâgavat Purânas; “Bra” signifies Brahmâ, Brahmânda and Brahmâvaivarta Purânas; “va” signifies Vâman, Vayu, Visnu and Varaha Purânas; “A” signifies Agni Purâna; “Na” signifies Narada Purâna; “Pa” signifies Padma Purâna; “Ling” signifies Linga Purânam; “Ga” signifies Govinda Purânam; Kû signifies Kurma Purâna and “Ska” signifies Skanda Purânam. These are the eighteen Purânas. O Saunaka! In the Matsya Purâna there are fourteen thousand slokas; in the wonderfully varied Markandeya Purânam there are nine thousand slokas. In the Bhavisya Purâna fourteen thousand and five hundred slokas are counted by the Munis, the seers of truth. In the holy Bhâgavata there are eighteen thousand S’lokas; in the Brahmâ Purâna there are Ajuta (ten thousand) S’lokas. In the Brahmânda Purâna there are twelve thousand one hundred S’lokas; in the Brahmâ Vaivarta Purânam there are eighteen thousand S’lokas. In the Vaman Purâna there are Ajuta (ten thousand) S’lokas; in the Vayu Purânam there are twenty-four thousand and six hundred S’lokas; in the greatly wonderful Visnu Purâna there are twenty-three thousand S’lokas; in the Agni Purânam there are sixteen thousand S’lokas; in the Brihat Narada Purânam, there are twenty-five thousand S’lokas, in the big Padma Purâna there are fifty-five thousand s'lokas; in the voluminous Linga Purâna eleven thousand s’lokas exist; in the Garuda Purânam spoken by Hari nineteen thousand s'lokas exist; iu the Kurma Purâna, seventeen thousand s'lokas exist and in the greatly wonderful Skanda Purâna there are eighty-one thousand s'lokas, O sinless Risis! Thus I have described to you the names of all the Purânas and the number of verses contained in them. Now hear about the Upa Purânas.
Upapuranas' names are as follows:
12-17. The first is the Upapurâna narrated by Sanat Kumâra; next comes Narasimha Purâna; then Naradiya Purâna, S’iva Purâna, Purâna narrated by Durvasa, Kapila Purâna, Manava Purâna, Aus’anasa Purâna, Varuna Purâna. Kalika Purâna, Samva Purâna, Nandi Kes’wara Purâna, Saura Purâna, Purâna spoken by Parâs’ara, Âditya Purâna, Mahesvara Purâna, Bhâgavata and Vasistha Purâna. These Upa Purânas are described by the Mahatmas.
For, the Upanishads, a minor Upanishad, called the Muktika (linked to the Shukla Yajurveda), gives a list of 108 of them:
The only means by which the final emancipation is at tained is through Mandukya-Upanishad alone, which is enough for the salvation of all aspirants. If Jnana is not attained thereby, study the 10 Upanishads; thou shalt soon attain Jnana, and then My Seat. son of Anjana, if thy Jnana is not made firm, practise (study) well the 32 Upanishads. Thou shalt get release. If thou longest after Videhamukti (or disembodied salvation), study the 108 Upanishads. I will truly state in order the (names of the) Upanishads with their S anti (purificatory Mantras). Hearken to them. (They are:) Is a, Kena, Katha, Prasna, Munda, Alandukya, Tittiri, Aitareya, Chhandogya, Brhadaranyaka, Brahma, Kaivalya, Jabala, S wetas watara, Hamsa, Arum, Garbha, Narayana, (Parama) -Hamsa, (Amrta)-Bindu, (Amrta)- Nada, (Atharva)-Sira, (AtharvaJ-Sikha, Maitrayani, Kaushitaki, (Brhat) Jabala, (Narasihma) -Tapani, Kiilagnirudra, Maitreyi, Subala, Kshurika, Mantrika, Sarvasara, Niralamba, (Suka)- Rahasya, Vajrasuchika, Tejo-(Bindu), Nada-(Bindu), Dhyana- (Bindu), (Brahma) -Vidya, Yoga-Tattwa, Atmabodhaka, Farivrat (Narada-Parivriijaka), (TraS ikhi, Sita, (Yoga)-Chuda-(Mani) Nirvana, Mandala-(Brahmana), pakshina-(Murti), Sarabha, Skanda, (Tripadvibhuti)-Maha-Narayana, Adwaya-(Taraka), (Rama)-Rahasya, (Rama) -Tapani, Vasudeva, Mudgala, S andilya, Paingala, Bhikshu, Mahat-Srariraka, (Yoga)-S ikha, Furiyatlta, Sannyasa, (Paramahamsa)-Parivrajaka, Akshamalika, Avyakta, Ekakshara, (Anna)-Purna, Surya, Akshi, Adhyatma, Kundika, Savitr, lAtma, Pas upata, Parabrahma, Avadhuta, Tripuratapani, Qe vi, Tripura, Kara, Bhavana, (Rudra) -Hrdaya, (Yoga) -Kundalini, Bhasma-(Jabala) Rudraksha, Ganapati, Darsana, Tarasara, Mahavakya, Panchabrahma, (Prana)-Agnihotra, Gopala-Tapani, Krshna, Yajnavalkya, Varaha, Satyayani, Hayagrlva, Dattatreya, Garuda, Kali-(Santarana), Jabala, Soubhagya, Saraswatirahasya, Bahvricha, and Muktika. These 108 (Upanishads) are able to do away with the three Bhavanas [of doubt, vain thought, and false thought] , conferring Jyana and Vairagya, and destroying the three Vasanas [of book-lore, world and body] .
From the Muktika Upanishad's 1st chapter.
As discussed in this answer, list of Maha Puranas is:
Vayu (includes Shiva Purana)
As per Kurma Puraana: Purvardha: Chapter 1, list of Upa Puranas is
The exhaustive list of Uppuranas from different sources is given in Ganesh Puran- Ek Addhyayan by Vineeta Devi: Chapter 1.
In his book, The Spiritual Heritage of India, Swami Prabhavananda writes in pages 135-6:
[footnote p 135] 'A Purana or sacred poetical work, supposed to be compiled or composed by the poet Vyasa; and comprising the whole body of Hindu theology; each Purana should treat of five topics especially: the creation, the destruction and renovation of the worlds; the genealogy of gods and heroes; the reigns of the Manus, and the transaction of their descendants; but great variety prevails in this respect and few contain historical or genealogical matter. There are eighteen acknowledged Puranas.' (Shabda-Sagara [Sanskrit-English Dictionary] by Pandit-Kulapati Jivananda Vidyasagara [Calcutta: Bhattacharyya, 1900].
and on page 135:
Altogether there are eighteen Puranas, six devoted to Visnu, six to Brahma, and six to Siva. All of them are written in verse, and all are usually attributed to Vyasa, the reputed author of the Mahabharata and editor of the Vedas. Their date may be safely assigned to the somewhat uncertain Epic Period.
A list of the 18 Puranas is on the Wikipedia site - https://en.wikipedia.org/wiki/Puranas. The other Puranas - the Upapuranas (other than those referred to as the 'Mahapuranas') are subject to disagreement, usually along sectarian lines.