Near-repdigit

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
4(10859669 - 1)2 - 2 1719338 p405 May 2022 Near - repdigit
58 · 101715905 - 1 1715906 L4879 Aug 2020 Near - repdigit
69992 · 101567410 - 1 1567414 L4879 Aug 2020 Near - repdigit
799 · 101536527 - 1 1536529 L4879 Feb 2019 Near - repdigit
8992 · 101533933 - 1 1533936 L4879 Feb 2019 Near - repdigit
992 · 101439761 - 1 1439763 L4789 Dec 2020 Near - repdigit
10(10657559 - 1)2 - 2 1315118 p405 May 2022 Near - repdigit
1193 · 101170023 - 1 1170025 L4789 Aug 2022 Near - repdigit
122 · 101059002 - 1 1059003 L3432 Sep 2013 Near - repdigit
1393 · 101029523 - 1 1029525 L4789 Jan 2019 Near - repdigit
149 · 101009567 - 1 1009568 L3735 Sep 2016 Near - repdigit
1596 · 10846519 - 1 846521 L2425 Sep 2011 Near - repdigit
1692 · 10833852 - 1 833854 L4789 Apr 2018 Near - repdigit
17(10393063 - 1)2 - 2 786126 p405 May 2022 Near - repdigit
18(10334568 - 1)2 - 2 669136 p405 May 2022 Near - repdigit
1993 · 10642225 - 1 642227 L4789 Mar 2020 Near - repdigit
208 · 10608989 - 1 608990 p297 May 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
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.