Are there any Puranas that are no more extant but known well?

Question

Currently, there are 18 mahapuranas and 18 upapuranas.

Is there any Purana, other than those above, whose name is well known and is no more extant? Or the total count is exactly 36?

Answer 1

The work, Studies in the Upapuranas, from the pen of Dr. R. C. Hazra, Professor of Smrti and Purana at Sanskrit College, Calcutta throws light on the number of upapuranas.

He says,

Following the tradition of the Mahapuranas, orthodox opinion tries to limit the number of the Upapuranas rigidly to ‘eighteen’ even in those cases where the promulgators of such opinion are fully conscious of the existence of a larger number; but while in the enumeration of the Puranas there is almost complete agreement with regard to the titles, this is by no means the case with the titles of the Upapuranas. In order to acquaint ourselves with the nature of the disagreement we give below a number of lists of ‘eighteen’ Upapuranas which we have been able to collect from different sources.

After listing all the names found in Puranas and Upapuranas, The author says:

From an examination of a large number of works, especially of the Sanskrit literature, we have been able to collect the names of mote than one hundred Upapuranas including those mentioned in the above lists. Questions relating to the identification, date and contents of these Upapuranas will be dealt with as fully as possible in their respective cases.

A glance over the above lists will show how greatly divergent the lists sometimes are. Though, as will be shown hereafter, the same Upapurana is in some cases mentioned in different lists under different titles, the above lists supply us with the titles of many more Upapuranas than eighteen.

Besides the Upapuranas mentioned in these lists, there were many others, of which some are available in printed forms, some still exist in manuscripts, some are known only from references and quotations, and some must have been lost altogether without leaving any trace of their existence. In spite of the serious loss that has been brought upon the Upapurana literature by the progress of time and the consequent changes in political administration as well as in the ideas, manners and customs of the people, the Upapuranic works are still rich in number and content.

You can download his work in two volumes here and here.

An upapurana Prabhasa Purana which Sanatan Goswami quotes twice in his works is not extant. But, of course, this purana is not well known. So, this may not be the example you are looking for.