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.

One protagonist in this novel spends a summer with the wife of Colonel Forster, and that character's aunt and uncle have the surname Gardiner. One character in this novel initially rejects a marriage proposal by Mr. Collins, while her sister is romanced by Mr. Bingley, and another romance in this novel is initiated by the master of Pemberley, Mr. Darcy. For 10 points, name this novel about the sisters of the Bennet family, one of whom is Elizabeth, by Jane Austen.
Literature

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.
Social Science

This novel contains two references to a character from Romeo and Juliet in the form of a prospective gift horse named Queen Mab. A trip to London reveals to one of the central characters that her love has been engaged to Sophia Grey, and other devastating news follows when it is learned that Lucy Steele has married, though we are deceived as to whom she married. However, the novel ends happily with the marriages of Colonel Brandon and Edward Ferrars to the heroines and John Willoughby nowhere to be found. FTP, identify this novel about Elinor and Marianne Dashwood written by Jane Austen.

Literature