Prospecting was the mining practice of searching for valuable materials. One who did this was known as a prospector. (TOS: "The Trouble with Tribbles")
In 2269, James T. Kirk asserted that if he did not receive the needed ryetalyn in one hour, he, Leonard McCoy, and Spock would go prospecting. (TOS: "Requiem for Methuselah")
In 2370, upon hearing of Alsia's plans to use her savings to buy the mining rights for the Vlugta asteroid belt, Martus Mazur questioned her wisdom, given the risk of prospecting. Alsia assured him that her father had conducted a full spectrum mineral analysis of the asteroids but didn't have the wherewithal to take advantage of the opportunity. (DS9: "Rivals")