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A fractal proof of the infinitude of primes. (English) Zbl 1460.11015

Summary: In this short paper, we give another proof of the infinitude of primes by using the upper box dimension, which is one of fractal dimensions.

MSC:

11A41 Primes
11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension
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References:

[1] H. Davenport, Multiplicative Number Theory, 2nd ed., Springer, New York, 1980. · Zbl 0453.10002 · doi:10.1007/978-1-4757-5927-3
[2] L. Euler, Variae observationes circa series infinitas, Commentarii Academiae Scientiarum Petropolitanae, 9:160-188, 1744.
[3] K. Falconer, Fractal Geometry: Mathematical Foundations and Applications, 3rd ed., JohnWiley & Sons, Chichester, 2014. · Zbl 1285.28011
[4] T.L. Heath, The Thirteen Books of Euclids Elements, Vol. 2, Cambridge Univ. Press, Cambridge, 1908.
[5] R. Meštrović, Euclid’s theorem on the infinitude of primes: A historical survey of its proofs (300 B.C.-2017) and another new proof, preprint, 2018, arXiv:1202.3670.
[6] J.C. Robinson, Dimensions, Embeddings, and Attractors, Cambridge Univ. Press, Cambridge, 2011. · Zbl 1222.37004
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