History
Euler stated that every arithmetic progression beginning with 1 contains an infinite number of primes. The theorem in the above form was first conjectured by Legendre in his attempted unsuccessful proofs of quadratic reciprocity and proved by Dirichlet in (Dirichlet 1837) with Dirichlet L-series. The proof is modeled on Euler's earlier work relating the Riemann zeta function to the distribution of primes. The theorem represents the beginning of rigorous analytic number theory.
Atle Selberg (1949) gave an elementary proof.
Read more about this topic: Dirichlet's Theorem On Arithmetic Progressions
Famous quotes containing the word history:
“The reverence for the Scriptures is an element of civilization, for thus has the history of the world been preserved, and is preserved.”
—Ralph Waldo Emerson (1803–1882)
“As I am, so shall I associate, and so shall I act; Caesar’s history will paint out Caesar.”
—Ralph Waldo Emerson (1803–1882)
“Humankind has understood history as a series of battles because, to this day, it regards conflict as the central facet of life.”
—Anton Pavlovich Chekhov (1860–1904)