Yes it is.  In fact there are five numbers with this
characteristic.  (10^n -1)/9 is prime when n is 2, 19, 23, 317 & 1031.
See "The Encyclopedia of Integer Sequences" sequence M2114, Neil J.A.
Sloane and Simon Plouffe, Academic Press, 1995.

Goto:  http://www.research.att.com/~njas/sequences/index.html

Sequentially yours,

Robert G. 'Bob' Wilson v,
PhD ATP / CFI
named my the authors as "our most prolific contributor on new
sequences."

"Kotera Hiroshi (Kotera Hiroshi)" wrote:

> Hi all
> Is a decimal 23-digit numbers 11111111111111111111111  prime ?
> Could you tell me the answer with proof?
>
> 24-digit numbers 11111111111111111111 = 101*1100110011001100110011
>
> regards
>
> ++++++++++++++++++++++++++++++++++++++++++
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> 630-8144$B!!F`NI;TEl6e>rD.(B1014-4
> phone : 0742-61-8521
> email : [EMAIL PROTECTED]
> URL : http://www.asahi-net.or.jp/~nj7h-ktr/
> ++++++++++++++++++++++++++++++++++++++++++
>
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