Primes

The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic. It has engaged the industry and wisdom of ancient and modern geometers to such an extent that it would be superfluous to discuss the problem at length…Further, the dignity of the science itself seems to require that every possible means be explored for the solution of a problem so elegant and so celebrated.
 

Disquisitiones Arithmeticae (1801)
Carl Friedrich Gauss (1777-1855)