FOM: Test Case for "Elementary" Proofs

Torkel Franzen torkel at
Thu Dec 11 10:30:59 EST 1997

  >Dirichlet's theorem (If n,k>1 have no common factor then the sequence [n+k,
  >n+2k,n+3k,n+4k, ... ] contains a prime) is much simpler to state than
  >the Prime Number Theorem, and unlike the P.N.T. no proof has ever
  >been found that does not go through complex analysis.

  An "elementary proof" is mentioned in the following reference:

  Hans Zassenhaus: Ueber die Existenz von Primzahlen in arithmetischen 
Progressionen. Comm. Math. Helv. 22 (1949), 232-259. The first elementary 
proof of Dirichlet's theorem.

  Is anybody familiar with this?

More information about the FOM mailing list