Primes that become composite after changing an arbitrary digit

Michael Filaseta, Jeremiah Southwick

Type: Article

Publication Date: 2020-09-02

Citations: 3

DOI: https://doi.org/10.1090/mcom/3593

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.

Locations

Mathematics of Computation - View - PDF

Similar Works

Action	Title	Year	Authors
+	Digitally delicate primes	2015	Jackson Hopper Paul Pollack
+	Consecutive primes which are widely digitally delicate	2021	Michael Filaseta Jacob Juillerat
+	Digitally delicate primes	2016	Jackson Hopper Paul Pollack
+	Digitally delicate primes	2015	Jackson Hopper Paul Pollack
+ PDF Chat	Consecutive primes which are widely digitally delicate	2022	Michael Filaseta Jacob Juillerat
+	A Note on Consecutive Composite Numbers	1961	Christian Grimm
+	The prime numbers	2014	Peter Coghill
+	Prime Numbers and Composite Numbers	2024
+ PDF Chat	An infinity of primes	2014	Joel Spencer
+	Repeatedly Appending Any Digit to Generate Composite Numbers	2019	Jon Grantham Witold Jarnicki John Rickert Stan Wagon
+	Primes numbers.	2011	Marie Washbrook
+	Prime and Composite Numbers	2021	Michal Křı́žek Lawrence Somer Alena Šolcová
+	Prime and Composite Numbers	2017
+	Prime Numbers in Prime Numbers Up To 5 Digits	2019	Inder J. Taneja
+	What are Prime Numbers?	2015	Barry Mazur William Stein
+	Primes	1986	Manfred R. Schroeder
+	Primes	1997	Manfred R. Schroeder
+	The Staircase of Primes	2015	Barry Mazur William Stein
+ PDF Chat	Composite positive integers with an average prime factor	2007	Florian Luca Francesco Pappalardi
+ PDF Chat	Primes with preassigned digits	2006	Glyn Harman

Works That Cite This (2)

Action	Title	Year	Authors
+ PDF Chat	Consecutive primes which are widely digitally delicate	2022	Michael Filaseta Jacob Juillerat
+	Finding a Widely Digitally Delicate Prime	2021	Jon Grantham

Works Cited by This (7)

Action	Title	Year	Authors
+ PDF Chat	On divisors of Lucas and Lehmer numbers	2013	C. L. Stewart
+ PDF Chat	Factorizations of 𝑏ⁿ±1, 𝑏=2, 3, 5, 6, 7, 10, 11, 12 Up to High Powers	1988	John Brillhart D. H. Lehmer J. L. Selfridge Bryant Tuckerman Samuel S. Wagstaff
+ PDF Chat	A REMARK ON PRIMALITY TESTING AND DECIMAL EXPANSIONS	2011	Terence Tao
+	On Pairwise Intersections of the Fibonacci, Sierpinski, and Riesel Sequences	2013	Dan Ismailescu Peter Seho Park
+	Digitally delicate primes	2016	Jackson Hopper Paul Pollack
+	Two Inquiries Related to the Digits of Prime Numbers	2020	Jeremiah Southwick
+	The on-line encyclopedia of integer sequences	2018	N. J. A. Sloane