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. Comments and suggestions requested.

(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
12 · 101059002 - 1 1059003 L3432 Sep 2013 Near - repdigit
296 · 10846519 - 1 846521 L2425 Sep 2011 Near - repdigit
38 · 10608989 - 1 608990 p297 May 2011 Near - repdigit
492 · 10544905 - 1 544907 L3735 May 2015 Near - repdigit
55 · 10511056 - 1 511057 p297 Mar 2011 Near - repdigit
695 · 10466002 - 1 466004 L3735 May 2014 Near - repdigit
75 · 10464843 - 1 464844 p297 Feb 2011 Near - repdigit
85 · 10445773 - 1 445774 p297 Jan 2011 Near - repdigit
96 · 10414508 - 1 414509 p297 Jan 2011 Near - repdigit
1010388080 - 10112433 - 1 388080 CH8 Nov 2014 Near - repdigit
1110388080 - 10180868 - 1 388080 p377 Nov 2014 Near - repdigit
1210388080 - 10332944 - 1 388080 p377 Dec 2014 Near - repdigit
1310388080 - 10342029 - 1 388080 p377 Dec 2014 Near - repdigit
149 · 10383643 - 1 383644 p297 Jan 2011 Near - repdigit
159999998 · 10369705 - 1 369712 L1958 Jan 2014 Near - repdigit
169 · 10364521 - 1 364522 p297 Dec 2010 Near - repdigit
179999992 · 10360403 - 1 360410 L1958 Nov 2011 Near - repdigit
1810360360 - 10183037 - 1 360360 p374 Mar 2014 Near - repdigit
1993 · 10359354 - 1 359356 L3735 Dec 2013 Near - repdigit
209999993 · 10335905 - 1 335912 L1958 Apr 2013 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 © 1996-2015 (all rights reserved)