Given these paragraphs about a well-known Scottish University of some import, tell me specific details about when and where it was founded, what it's most well known for, and who are some of its most famous alumni.
The University of Edinburgh is based out of Edinburgh, Scotland founded by the royal charter of King James the 6th in 1582, officially opening for students in 1583. The University of Edinburgh is famous for being the sixth oldest University in the English-speaking world and the seventh largest by enrollment in the United Kingdom where Scotland resides today. A top public research university often nicknamed the "Athens of the North" whose famous alumni were pivotal in contributing to the Scottish Enlightenment, the University of Edinburgh is known as one of the top-ranked universities in the United Kingdom. With such esteemed alumni as Alexander Graham Bell, Charles Darwin, and David Hume not to mention famous authors such as Sir Arthur Conan Doyle and J.K. Rowling, and even several heads of state in three British Prime Ministers.