Peridot is forsteritic olivine that is of gem quality. It only occurs in one color - transparent olive green, and it has the chemical formula (Mg,Fe)2SiO4. Olivine is made up of forsterite (Mg2SiO4) and fayalite (Fe2SiO4) in varying amounts - in what is known as a "solid solution". Peridot being described as forsteritic means that it is by definition more than 50% forsterite.  However, the rich green color is cause by the iron in the mineral.
Emerald Cut Peridot
Olivine is one of the earth's most common minerals  - but most of it is not of gem quality and peridot is somewhat rare. Olivine is also sometimes known as chrysolite, although this can cause confusion as chrysolite was also an old name for chrysoberyl. 
Peridot has a hardness of 6.5-7 on the Mohs scale - yet is known to be difficult to cut owing to brittleness.
Peridot is another gemstone with an ancient history of use. It has been found in Egyptian jewelry dating back to almost 2,000 BC, and was mentioned as one of the stones of the High Priest's Breastplate in the Bible. It was also prized by the Romans and used in medieval times. However, most of the early sources of peridot ran out, and after the baroque period faded in popularity. 
Peridot has a history of being confused with emerald - and some of the emeralds belonging to the famous Cleopatra are suspected to have been peridots. 
In the 1990s however, peridot saw a resurgence in popularity - due to a spectacular, rich find of the finest quality peridot yet discovered, in the mountains of the Pakistan / Afghanistan border. These stones have become known as "Kashmir Peridots". 
Peridot is mined in a handful of places - with mines being listed in Burma (Myanmar), Canada, China, Egypt, Ethiopia, France, New Caledonia (in the southwest Pacific), Norway, Pakistan, Brazil, Spain and the USA.   The mines in Myanmar (formerly Burma) once supplied high quality peridot gems, however Myanmar is no longer considered to be a major supplier, and it's said that since the socialist government rose to power, the supply has been curtailed - for reasons unknown to the west. The majority of the world's peridot (80-95%) comes from the San Carlos Apache Indian Reservation in Arizona, USA.
Peridot is readily available for purchase online through various outlets - and "general" prices range from around $25-$100 per carat for stones in the 2-10 carat range. However, as with other colored stones, prices are very diverse depending on color and clarity: Prices "fall through the floor" for lesser quality stones, and go up through the roof for the best ones - with prices for flawless stones in the 50 carat range going over $500 per carat.
The largest cut peridot in the world is said by many sources to be the 310 carat gem in the Gem and Mineral Collection at the Smithsonian's National Museum of Natural History in the USA. However,  mentions a 319 carat gem from Myanmar (Burma) although further details are not given.
The most ancient source of peridot, Zabargad Island, which used to be called Saint John's Island, still produces peridot. This island was mentioned by Pliny the Elder in AD 70 in his book Naturalis Historiae.
Peridot is the "birthstone" for the month of August.
Peridot - Sources Referenced:
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