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: To isolate volatile compounds from nonvolatile impurities, the steam form of this process is used when the compounds decompose at standard temperatures and pressures. Two miscible liquids are heated under a Liebig condenser to increase the concentration of the liquid with the lower boiling point in a common type of this process. FTP, name this separation method by boiling point, whose fractional variety yields cosmetics from petroleum and alcohol from a water mixture.

SOLUTION: Science

PROBLEM: This ruler was supposedly punished by a deity with famine after suppressing a revolt in Subartu, and he had earlier dealt with an invasion led by four great Elamite generals. He began his reign following the defeat of a King of Umma, Lugulzaggesi, who had fought a war against Ur-Zababa. After taking Kish from Lugulzaggesi, he built his empire by extending trade from his capital city throughout to Susa and the Zagros mountains. He was succeeded by his sons Rimush and Manishtushu, and made his daughter Enheduanna the high priestess of Nanna. For 10 points, name this former sandal-bearer, a possible inspiration for the biblical Nimrod, a great king of Akkad.

SOLUTION:
History