The Top Twenty--a Prime Page Collection

Near-repdigit

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The Prime Pages keeps a list of the 5000 largest known primes, plus a few each of certain selected archivable forms and classes. These forms are defined in this collection's home page.This page is about one of those forms.

(up) Definitions and Notes

A repunit is a number of the form 11111...111 (repeated units). In base two (binary), these are the Mersenne primes. In base ten, just a few are known. If we repeat any other digit, then we get a composite (e.g., 777777 is divisible by 7).

To get a more general form, two things have been tried:

  1. Let one of the digits differ from one--these are the near repunit primes.
  2. Let all but one of the digits be the same, these are the near repdigit primes (and include the near repunit primes).

(up) Record Primes of this Type

rankprime digitswhowhencomment
1101888529 - 10944264 - 1 1888529 p423 Oct 2021 Near - repdigit, palindrome
2993 · 101768283 - 1 1768286 L4879 Feb 2019 Near - repdigit
39 · 101762063 - 1 1762064 L4879 Aug 2020 Near - repdigit
48 · 101715905 - 1 1715906 L4879 Aug 2020 Near - repdigit
59992 · 101567410 - 1 1567414 L4879 Aug 2020 Near - repdigit
699 · 101536527 - 1 1536529 L4879 Feb 2019 Near - repdigit
7992 · 101533933 - 1 1533936 L4879 Feb 2019 Near - repdigit
892 · 101439761 - 1 1439763 L4789 Dec 2020 Near - repdigit
92 · 101059002 - 1 1059003 L3432 Sep 2013 Near - repdigit
1093 · 101029523 - 1 1029525 L4789 Jan 2019 Near - repdigit
119 · 101009567 - 1 1009568 L3735 Sep 2016 Near - repdigit
1296 · 10846519 - 1 846521 L2425 Sep 2011 Near - repdigit
1392 · 10833852 - 1 833854 L4789 Apr 2018 Near - repdigit
1493 · 10642225 - 1 642227 L4789 Mar 2020 Near - repdigit
158 · 10608989 - 1 608990 p297 May 2011 Near - repdigit
1692 · 10544905 - 1 544907 L3735 May 2015 Near - repdigit
175 · 10511056 - 1 511057 p297 Mar 2011 Near - repdigit
1895 · 10466002 - 1 466004 L3735 May 2014 Near - repdigit
195 · 10464843 - 1 464844 p297 Feb 2011 Near - repdigit
205 · 10445773 - 1 445774 p297 Jan 2011 Near - repdigit

(up) References

Caldwell89
C. Caldwell, "The near repdigit primes 333 ... 331," J. Recreational Math., 21:4 (1989) 299--304.
Caldwell90
C. Caldwell, "The near repdigit primes AnB, ABn, and UBASIC," J. Recreational Math., 22:2 (1990) 100--109.
CD95
C. Caldwell and H. Dubner, "The near repunit primes 1n-k-1011k," J. Recreational Math., 27 (1995) 35--41.
CD97
C. Caldwell and H. Dubner, "The near repdigit primes An-k-1B1Ak, especially 9n-k-1819k," J. Recreational Math., 28:1 (1996-97) 1--9.
Heleen98
Heleen, J. P., "More near-repunit primes 1n-k-1D11k, D=2,3, ..., 9," J. Recreational Math., 29:3 (1998) 190--195.
Williams78b
H. C. Williams, "Some primes with interesting digit patterns," Math. Comp., 32 (1978) 1306--1310.  Corrigendum in 39 (1982), 759.  MR 58:484
Chris K. Caldwell © 1996-2022 (all rights reserved)