# 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. Comments and suggestions requested.

### 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).

### Record Primes of this Type

rankprime digitswhowhencomment
12 · 101059002 - 1 1059003 L3432 Sep 2013 Near - repdigit
29 · 101009567 - 1 1009568 L3735 Sep 2016 Near - repdigit
396 · 10846519 - 1 846521 L2425 Sep 2011 Near - repdigit
492 · 10833852 - 1 833854 L4789 Apr 2018 Near - repdigit
58 · 10608989 - 1 608990 p297 May 2011 Near - repdigit
692 · 10544905 - 1 544907 L3735 May 2015 Near - repdigit
75 · 10511056 - 1 511057 p297 Mar 2011 Near - repdigit
895 · 10466002 - 1 466004 L3735 May 2014 Near - repdigit
95 · 10464843 - 1 464844 p297 Feb 2011 Near - repdigit
105 · 10445773 - 1 445774 p297 Jan 2011 Near - repdigit
116 · 10414508 - 1 414509 p297 Jan 2011 Near - repdigit
1299998 · 10389150 - 1 389155 L3432 Sep 2016 Near - repdigit
1310388080 - 10112433 - 1 388080 CH8 Nov 2014 Near - repdigit
1410388080 - 10180868 - 1 388080 p377 Nov 2014 Near - repdigit
1510388080 - 10332944 - 1 388080 p377 Dec 2014 Near - repdigit
1610388080 - 10342029 - 1 388080 p377 Dec 2014 Near - repdigit
1799999995 · 10386956 - 1 386964 L3432 Sep 2016 Near - repdigit
189 · 10383643 - 1 383644 p297 Jan 2011 Near - repdigit
199999998 · 10369705 - 1 369712 L1958 Jan 2014 Near - repdigit
209 · 10364521 - 1 364522 p297 Dec 2010 Near - repdigit

### 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