your pearls sound lovely and the 10k mark on the clasp would be the gold content of the metal. As the strand of pearls were your great grandmothers then there is the possibility that they may have been restrung at some stage.
The quality of the clasp however, can be a clue to the quality of the pearls but by no way definitive. If the pearls are individually knotted this will be a clue - good quality pearls, in most cases will have a knot between each pearl to protect the pearls from rubbing against each other.
Pearls can be natural (natural pearls are the most rare and the most expensive) cultured, freshwater and faux pearls. When considering the value of antique pearls you need to have in mind the Mikimoto time line.
Mikimoto's business began to expand rapidly after 1916. Mikimoto was the first to market cultured pearls successfully. If the pearls predate the 1900s they are freshwater or synthetic or if you're lucky - natural pearls.
The only definitive test to determine if the strand is comprised of natural pearls is to have them x-rayed ( not the dentist kind of x-ray) GIA are able to test pearls.
The new cultured pearling technology enabled Japan's cultured pearl industry to quickly expand after 1916, and by 1935 there were 350 pearl farms in Japan producing 10 million cultured pearls annually.
Before you can value a strand of pearls, the type of pearl has to be determined first. Here is some more info Lee on different types of pearls:
