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:
“It is remarkable how closely the history of the apple tree is connected with that of man.”
—Henry David Thoreau (1817–1862)
“There is no example in history of a revolutionary movement involving such gigantic masses being so bloodless.”
—Leon Trotsky (1879–1940)
“There are two great unknown forces to-day, electricity and woman, but men can reckon much better on electricity than they can on woman.”
—Josephine K. Henry, U.S. suffragist. As quoted in History of Woman Suffrage, vol. 4, ch. 15, by Susan B. Anthony and Ida Husted Harper (1902)