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The search for a finite projective plane of order 10. (English) Zbl 0744.51011

This paper describes the history and how computers were used to solve the problem of the existence of a projective plane of order 10. It starts with a review of some general existence theorems on finite projective planes. The author then explains how the problem on the plane of order 10 is reduced to a form suitable for a computer. All major steps are mentioned, including the final difficulties (when, after the kill, some mistakes were detected but, fortunately, repaired). The paper ends with some remarks on the reliability of a proof by computer and in particular this proof.

MSC:

51E15 Finite affine and projective planes (geometric aspects)
51-02 Research exposition (monographs, survey articles) pertaining to geometry
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Online Encyclopedia of Integer Sequences:

Number of nonisomorphic projective planes of order n.