TASK DEFINITION: In this task you will be given a text passage from a trivia quiz. You should choose the category this question belongs to from these categories: History, Science, Social Science, Fine Arts, Literature. You can only choose one category, so if in doubt, please choose the closest match.
PROBLEM: Paulo Ribenboim proved in 1991 that the set of these is Diophantine, and in 1912 Edmund Landau proposed four "unattackable problems" dealing with them, none of which have yet been solved. The theorem named for them states that the number of them less than or equal to n is approximately equal to n divided by the natural logarithm of n. The GIMPS project seeks to find examples of the Mersenne type of this number, ordinary examples of which can be found using the sieve of Eratosthenes. For 10 points, identify these numbers whose only two factors are 1 and itself.

SOLUTION: Social Science

PROBLEM: One commander killed in this engagement invented a beech-loading rifle that had earlier been used in the Battle of Brandywine. The Patriot commanders in this battle utilized shifting positions along the base of the central topological entity in this battle, while the leading Loyalist officer's decision to put on a plaid shirt to cover his officer's colors resulted in his demise, as Patriot snipers trained their sights onto the shirt. Colonels John Sevier and William Campbell led part of the Patriot attack at this engagement, and were opposed by Major Patrick Ferguson's force of roughly 1,100 Loyalists. For 10 points, name this Patriot victory in the American Revolution in North Carolina, which followed Horatio Gates' defeat at Camden.

SOLUTION: History

PROBLEM: In 1751, he wrote "Letter on the Deaf and Dumb" which studied the function of language, while two years later he published "An Essay on Blindness" which advocated teaching the blind to read a century before Braille. Notable plays include "The Test of Virtue" and "The Father of the Family", and his theories on drama advocating greater realism on the stage greatly influenced Gotthold Ephraim Lessing. He wrote the philosophical treatise "D'Alembert's Dream" and collaborated with D'Alembert to compile a work which would bring out the essential principles and applications of every art and science. FTP, who is mainly known for "The Encyclopedie. "

SOLUTION:
Social Science