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 variant of this phenomenon can be used to tune the electronic properties of boron nitride nanotubes from nearly insulating to metallic. Another variant of this phenomenon is induced by interference of standing laser waves to trap atoms of a Bose-Einstein condensate loaded into an optical lattice. Schrdinger's third article from his 1926 series of papers presented his perturbation theory treatment of this effect's modification of the Balmer and Lyman series. Along with van der Waals broadening and resonance broadening, this effect can produce pressure broadening of spectral lines. In addition to the giant version and the AC or Autler-Townes form of this effect, it exhibits variants that are linear and quadratic in the applied field. FTP name this shifting and splitting of spectral lines due to an external electric field, the analogue of the Zeeman effect.

SOLUTION: Science

PROBLEM: Its precursor, the Distribution Act, increased the money supply by distributing the accumulated federal surplus to the states, but the effect spurred deflation and caused a seven-year depression. Issued by treasury secretary Levi Woodbury, it was the largest attack of the president's war against the Second Bank of the United States as well as state "pet banks. "  Though specifically targeted only at those profiting unfairly from government land transactions, FTP, name this 1837 executive order by Andrew Jackson that made only gold and silver payments acceptable.

SOLUTION:
History