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:
“In all history no class has been enfranchised without some selfish motive underlying. If to-day we could prove to Republicans or Democrats that every woman would vote for their party, we should be enfranchised.”
—Carrie Chapman Catt (1859–1947)
“In the history of the human mind, these glowing and ruddy fables precede the noonday thoughts of men, as Aurora the sun’s rays. The matutine intellect of the poet, keeping in advance of the glare of philosophy, always dwells in this auroral atmosphere.”
—Henry David Thoreau (1817–1862)
“Properly speaking, history is nothing but the crimes and misfortunes of the human race.”
—Pierre Bayle (1647–1706)