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)
“To summarize the contentions of this paper then. Firstly, the phrase ‘the meaning of a word’ is a spurious phrase. Secondly and consequently, a re-examination is needed of phrases like the two which I discuss, ‘being a part of the meaning of’ and ‘having the same meaning.’ On these matters, dogmatists require prodding: although history indeed suggests that it may sometimes be better to let sleeping dogmatists lie.”
—J.L. (John Langshaw)
“The history of this country was made largely by people who wanted to be left alone. Those who could not thrive when left to themselves never felt at ease in America.”
—Eric Hoffer (1902–1983)