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: These quantities are the arguments of the logarithms in the von Mangoldt function, which is itself summed to yield the second Chebyshev function. Using the evenly-spaced integer topology, Furstenberg re-proved that there were aleph-null many of these values. The work of Goldston et al. employing the Elliott-Halberstam conjecture was a precursor to Zhang's proof of bounded gaps between them. Thanks to the AKS algorithm, it is polytime-decidable whether or not a number is one of these numbers. The distribution of these numbers is described by the law "pi of x is asymptotic to x over log x," where "pi of x" is the function that counts these numbers. They are typically generated by sieving, as originally done by Eratosthenes. For 10 points, what numbers are divisible only by one and themselves

SOLUTION: Science

PROBLEM: Fascinated in his youth by the sea and ships, he spent two years of his reign traveling throughout Europe learning the techniques of shipbuilding, but upon his return was forced to put down a revolt of the streltsy. Originally joint emperor with his retarded brother Ivan under the regency of his half-sister Sophia, he soon seized power, and later had his son Alexei tortured to death to maintain his rule. His seizure and eventual loss of Azov was his first notable attempt to gain greater maritime access, which was completed with his gain of a section of the Baltic coast, where he founded his new capital, modeled on the Western ideas he forced upon his country. FTP, who was this victor in the Great Northern War who from 1682-1725 ruled Russia

SOLUTION: History

PROBLEM: A focal point of engagements in this conflict was the fort at Labdalum, and it culminated in a slaughter at the Assinarus River. Walls of circumvallation were built outward from the Epipolae plateau, and Lamachus was killed during a raid on a counter-wall. Superstition over a lunar eclipse caused the attackers to fail to retreat when they had the chance, after which the survivors were left to die in nearby quarries. The official pretext of this conflict was to attack Selinus in support of Segesta. Led by Nicias, it began with the defection of its instigator to Sparta and ended with a disastrous siege of Syracuse. For 10 points, name this phase of the Peloponnesian War supported by Alcibiades, an Athenian expedition to an Italian island.

SOLUTION:
History