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- W2952162802 abstract "We show that for any fixed base $a$, a positive proportion of primes have the property that they become composite after altering any one of their digits in the base $a$ expansion; the case $a=2$ was already established by Cohen-Selfridge and Sun, using some covering congruence ideas of ErdH{o}s. Our method is slightly different, using a partially covering set of congruences followed by an application of the Selberg sieve upper bound. As a consequence, it is not always possible to test whether a number is prime from its base $a$ expansion without reading all of its digits. We also present some slight generalisations of these results." @default.
- W2952162802 created "2019-06-27" @default.
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- W2952162802 date "2008-02-22" @default.
- W2952162802 modified "2023-10-16" @default.
- W2952162802 title "A remark on primality testing and decimal expansions" @default.
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- W2952162802 doi "https://doi.org/10.48550/arxiv.0802.3361" @default.
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