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arXiv · 1812.07650

Extending Babbage's (Non-)Primality Tests

Jonathan Sondow
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Abstract

We recall Charles Babbage's 1819 criterion for primality, based on simultaneous congruences for binomial coefficients, and extend it to a least-prime-factor test. We also prove a partial converse of his non-primality test, based on a single congruence. Two problems are posed. Along the way we encounter Bachet, Bernoulli, Bezout, Euler, Fermat, Kummer, Lagrange, Lucas, Vandermonde, Waring, Wilson, Wolstenholme, and several contemporary mathematicians.

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Jonathan Sondow. 2018-12-18. Extending Babbage's (Non-)Primality Tests. https://arxiv.org/abs/1812.07650

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