A formalized proof of Dirichlet's theorem on primes in arithmetic progression

Journal of Formalized Reasoning, vol. 2, number 1, pp. 63-83, 2009.

Abstract:

We describe the formalization using the HOL Light theorem prover of Dirichlet's theorem on primes in arithmetic progression. The proof turned out to be more straightforward than expected, but this depended on a careful choice of an informal proof to use as a starting-point. The goal of this paper is twofold. First we describe a simple and efficient proof of the theorem informally, which is otherwise difficult to find in one self-contained place at an elementary level. We also describe its, largely routine, HOL Light formalization, a task that took only a few days.

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Bibtex entry:

@ARTICLE{harrison-dirichlet,
        author          = "John Harrison",
        title           = "A formalized proof of {D}irichlet's theorem on
                           primes in arithmetic progression",
        journal         = "Journal of Formalized Reasoning",
        volume          = 2,
        number          = 1,
        year            = 2009,
        pages           = "63--83"}