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Near-repdigit
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Let me know if something in the Top20 is not working (caldwell@utm.edu).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.
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:
- Let one of the digits differ from one--these are the
near repunit primes.
- 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
| rank | prime |
digits | who | when | comment |
|---|
| 1 | 101888529 - 10944264 - 1 |
1888529 |
p423 |
Oct 2021 |
Near - repdigit, palindrome |
| 2 | 993 · 101768283 - 1 |
1768286 |
L4879 |
Feb 2019 |
Near - repdigit |
| 3 | 9 · 101762063 - 1 |
1762064 |
L4879 |
Aug 2020 |
Near - repdigit |
| 4 | 8 · 101715905 - 1 |
1715906 |
L4879 |
Aug 2020 |
Near - repdigit |
| 5 | 9992 · 101567410 - 1 |
1567414 |
L4879 |
Aug 2020 |
Near - repdigit |
| 6 | 99 · 101536527 - 1 |
1536529 |
L4879 |
Feb 2019 |
Near - repdigit |
| 7 | 992 · 101533933 - 1 |
1533936 |
L4879 |
Feb 2019 |
Near - repdigit |
| 8 | 92 · 101439761 - 1 |
1439763 |
L4789 |
Dec 2020 |
Near - repdigit |
| 9 | 2 · 101059002 - 1 |
1059003 |
L3432 |
Sep 2013 |
Near - repdigit |
| 10 | 93 · 101029523 - 1 |
1029525 |
L4789 |
Jan 2019 |
Near - repdigit |
| 11 | 9 · 101009567 - 1 |
1009568 |
L3735 |
Sep 2016 |
Near - repdigit |
| 12 | 96 · 10846519 - 1 |
846521 |
L2425 |
Sep 2011 |
Near - repdigit |
| 13 | 92 · 10833852 - 1 |
833854 |
L4789 |
Apr 2018 |
Near - repdigit |
| 14 | 93 · 10642225 - 1 |
642227 |
L4789 |
Mar 2020 |
Near - repdigit |
| 15 | 8 · 10608989 - 1 |
608990 |
p297 |
May 2011 |
Near - repdigit |
| 16 | 92 · 10544905 - 1 |
544907 |
L3735 |
May 2015 |
Near - repdigit |
| 17 | 5 · 10511056 - 1 |
511057 |
p297 |
Mar 2011 |
Near - repdigit |
| 18 | 95 · 10466002 - 1 |
466004 |
L3735 |
May 2014 |
Near - repdigit |
| 19 | 5 · 10464843 - 1 |
464844 |
p297 |
Feb 2011 |
Near - repdigit |
| 20 | 5 · 10445773 - 1 |
445774 |
p297 |
Jan 2011 |
Near - repdigit |
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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