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: In his later work he distinguished between value that is invoked when an interpersonal exchange occurs and value as denoting the qualitative mental evaluation of elements. Using these definitions, he created an algebra of social exchange in his Sociological Studies. In his earlier work he argued that information processing is guided by a need for equilibrium, which is restored by either assimilating new information into old patterns, or altering the old pattern to accommodate the new information. Known for his belief in instinctual "schemas" of behavior at birth, he sought to understand the formation of knowledge in terms of "genetic epistemology. " FTP, name this French developmental psychologist, best known for positing four stages of development beginning with the sensorimotor.

SOLUTION: Social Science

PROBLEM: This man was imprisoned by Protestant nobles during the Ruthven Raid, and his early reign saw the Battle of Langside and was dominated the Earl of Morey, who served as this man's regent. This son of Lord Darnley married Anne of Denmark. An attempt by Catholic Priests to kidnap this man is known as the Bye Plot, while the Main Plot was hatched by Protestants who wanted to replace him with his cousin Arbella. This king's attempt to find a Habsburg bride for his son was known as the "Spanish Match". This author of "The Trew Law of Free Monachy" was also targeted by Catesby and Fawkes in the Gunpower Plot. For ten points, name this Stuart, the first man to rule both England and Scotland, who lends his name to a Bible.

SOLUTION:
History