FOM: Test Case for "Elementary" Proofs
Torkel Franzen
torkel at sm.luth.se
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?
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