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The most reliable way to find gems on Runescape (other than buying them on the
Grand Exchange, of course) is to mine gem rocks. Gem rocks can be found in
Shilo Village and in the Lunar Mine, but you'll have to complete the associated quests in order to have access to them. Also, there is an additional mine with gem rocks under Shilo Village that can be accessed by those who have finished the hard portion of the Karamja Achievement diary.
Another special kind of gem rock can be found when playing the Tai Bwo Wannai Cleanup minigame. These rocks appear randomly, and each one can be mined thrice to receive three gems.
When mining gem rocks, it's possible to obtain one of the following gems: jade, opal, sapphire, emerald, ruby, diamond, or red topaz. If you're planning to cut the gems anyway, it's a good idea to take a chisel along with you when you mine gem rocks. This way, you can cut the gems while waiting for the gems to respawn. If you accidentally crush them, you can just drop the crushed gem to make room in your inventory for more.