There are several mysteries about a 101.84-carat pure white diamond that has turned up out of nowhere and which Sotheby's is to sell in Geneva next month.

No one knows - or is saying - where it was found, though it's rumored to come from Botswana. The diamond is supposed to have changed hands serveral times on its journey out of Africa, rising in value from $100,000 for the raw rock to several million by the time it reached Belgium.And no one is saying who cut it, though this almost certainly took place in Antwerp during the summer. It is a major coup for the cutters, for they have brought the stone to market above the magic 100-carat mark, even though the uncut stone was only 222.30 carats.

The raw stone was boiled in acid for several days to clear away surface occlusions so that the cutters could study the internal structure. The cutting and polishing took at least seven weeks. But the main mystery is, of course, how much the stone will fetch when it is auctioned on Nov. 14.

Traditionally, jewelry does well in times of turbulence. So if war were to break out in the Persian Gulf region, this huge stone could look even more alluring than it does already. Alternatively, a prolonged shooting war could frighten off many of the private collectors who are otherwise expected to bid.

The current auction record is $9.1 million, for an 85-carat D-flawless diamond sold at Sotheby's in 1988. In normal circumstances, this new stone would be expected to break that record comfortably. A figure of $13 million has been mentioned.

There are only 16 pure white diamonds known that are bigger than this one, including Cullinan I, at 530.2 carats; the Jublilee, at 245.35 carats, and the Niarchos, at 128.25 carats.

The new diamond lacks a name as yet.