The Top Twenty--a Prime Page Collection

Near-repdigit

This page : Definition(s) | Records | References | RSS 2.0 Feed
  View this page in:   language help
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
45 · 10511056 - 1 511057 p297 Mar 2011 Near - repdigit
595 · 10466002 - 1 466004 L3735 May 2014 Near - repdigit
65 · 10464843 - 1 464844 p297 Feb 2011 Near - repdigit
75 · 10445773 - 1 445774 p297 Jan 2011 Near - repdigit
86 · 10414508 - 1 414509 p297 Jan 2011 Near - repdigit
99 · 10383643 - 1 383644 p297 Jan 2011 Near - repdigit
109999998 · 10369705 - 1 369712 L1958 Jan 2014 Near - repdigit
119 · 10364521 - 1 364522 p297 Dec 2010 Near - repdigit
129999992 · 10360403 - 1 360410 L1958 Nov 2011 Near - repdigit
1310360360 - 10183037 - 1 360360 p374 Mar 2014 Near - repdigit
1493 · 10359354 - 1 359356 L3735 Dec 2013 Near - repdigit
159999993 · 10335905 - 1 335912 L1958 Apr 2013 Near - repdigit
169999993 · 10331938 - 1 331945 L1958 Apr 2013 Near - repdigit
176 · 10319889 - 1 319890 p297 Nov 2010 Near - repdigit
1810314727 - 8 · 10157363 - 1 314727 p235 Jan 2013 Near - repdigit, palindrome
19992 · 10312136 - 1 312139 p356 Apr 2013 Near - repdigit
206 · 10293134 - 1 293135 p297 Nov 2010 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 © 1996-2014 (all rights reserved)