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Mathematics of Computation

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Primes that become composite after changing an arbitrary digit


Authors: Michael Filaseta and Jeremiah Southwick
Journal: Math. Comp. 90 (2021), 979-993
MSC (2020): Primary 11Y11; Secondary 11A63, 11N36, 11P32, 11Y05
DOI: https://doi.org/10.1090/mcom/3593
Published electronically: November 24, 2020
MathSciNet review: 4194171
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Abstract: We show that a positive proportion of the primes have the property that if any one of its digits in base $10$, including its infinitely many leading $0$ digits, is replaced by a different digit, then the resulting number is composite.


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Additional Information

Michael Filaseta
Affiliation: Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208
MR Author ID: 66800
Email: filaseta@math.sc.edu

Jeremiah Southwick
Affiliation: Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208
ORCID: 0000-0003-0751-8358
Email: soutjt14@alumni.wfu.edu

Keywords: Covering system, digitally delicate primes, density, sieve
Received by editor(s): January 13, 2020
Received by editor(s) in revised form: January 30, 2020, and July 29, 2020
Published electronically: November 24, 2020
Article copyright: © Copyright 2020 American Mathematical Society