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This is the Prime Pages'
interface to our BibTeX database. Rather than being an exhaustive database,
it just lists the references we cite on these pages. Please let me know of any errors you notice.References: [ Home  Author index  Key index  Search ]
 TT2011
 Tao, Terence, "A remark on primality testing and decimal expansions," J. Aust. Math. Soc., 91:3 (2011) 405413. (http://dx.doi.org/10.1017/S1446788712000043) MR 2900615
Abstract:
We show that for any fixed base a, a positive proportion of primes become composite after any one of their digits in the base a expansion is altered; the case where a=2 has already been established by Cohen and Selfridge [`Not every number is the sum or difference of two prime powers', Math. Comput. 29 (1975), 7981] and Sun [`On integers not of the form ± p^{a} ± q^{b}', Proc. Amer. Math. Soc. 128 (2000), 9971002], using some covering congruence ideas of ErdÅ‘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.
