instruction:
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.
question:
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.
answer:
Social Science

question:
A weight of the nth power of this parameter is imputed to contributions to elements of an S matrix by nth-order Feynman diagrams; thus, this number can be considered the order of expansion in perturbative quantum electrodynamics. This constant is a measure of the electron anomalous magnetic moment, which explains its role in the relativistic splitting of atomic spectral lines that is its namesake. The coupling constant for the electromagnetic interactions of electrons, it is equal to the square of the ratio of the electron and Planck charges, or, in cgs units, the electron charge squared divided by the speed of light times Diracs constant. For ten points, name this physical constant usually denoted alpha and equal to about one over one hundred thirty-seven.
answer:
Science

question:
Its creator described it as "very loud and noisy," and admitted that he was only interested in the lucrative commission. Composed for the consecration of the Cathedral of Christ the Savior for the 1882 Moscow Exhibition, it debuted on August 20th to immediate accolades, and was eventually made the composer's Opus number 49. Using the Marseillaise and the Tsarist national anthem to depict two armies, it uses bells, cannons, and a fireworks finale to commemorate the 70th anniversary of the Battle of Borodino. FTP, name this famous Tchaikovsky overture named for the year Borodino was fought.
answer:
Fine Arts