Paper
Ours go to 211: Euler pseudoprimes to 47 prime bases (from Carmichael numbers)
Authors
Alejandra Alcantarilla Sánchez, Jolijn Cottaar, Tanja Lange, Benne de Weger
Abstract
In this paper we show that a certain subset of the Carmichael numbers contains good Euler pseudoprimes, composite numbers that for many bases survive the Solovay-Strassen primality test. We present a classification of Carmichael numbers, and use the knowledge gained from this to create a fast algorithm to compute new Euler pseudoprimes, by multiplying already found Euler pseudoprimes. We use this algorithm to find many Euler pseudoprimes that are pseudoprimes for several consecutive prime bases starting at 2, hence for all integer bases up to that number. The best Euler pseudoprime we find survives up to 211, i.e., survives the first 47 prime bases.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2602.21840v1</id>\n <title>Ours go to 211: Euler pseudoprimes to 47 prime bases (from Carmichael numbers)</title>\n <updated>2026-02-25T12:20:12Z</updated>\n <link href='https://arxiv.org/abs/2602.21840v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2602.21840v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>In this paper we show that a certain subset of the Carmichael numbers contains good Euler pseudoprimes, composite numbers that for many bases survive the Solovay-Strassen primality test. We present a classification of Carmichael numbers, and use the knowledge gained from this to create a fast algorithm to compute new Euler pseudoprimes, by multiplying already found Euler pseudoprimes. We use this algorithm to find many Euler pseudoprimes that are pseudoprimes for several consecutive prime bases starting at 2, hence for all integer bases up to that number. The best Euler pseudoprime we find survives up to 211, i.e., survives the first 47 prime bases.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='math.NT'/>\n <published>2026-02-25T12:20:12Z</published>\n <arxiv:comment>21 pages, 2 figures</arxiv:comment>\n <arxiv:primary_category term='math.NT'/>\n <author>\n <name>Alejandra Alcantarilla Sánchez</name>\n </author>\n <author>\n <name>Jolijn Cottaar</name>\n </author>\n <author>\n <name>Tanja Lange</name>\n </author>\n <author>\n <name>Benne de Weger</name>\n </author>\n </entry>"
}