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A Prime 
 for which 
 has a maximal period Decimal Expansion of 
 Digits.  The first
few numbers with maximal decimal expansions are 7, 17, 19, 23, 29, 47, 59, 61, 97, ... (Sloane's A001913).
References
Sloane, N. J. A.  Sequence
A001913/M4353
in ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.
The Encyclopedia of Integer Sequences.  San Diego: Academic Press, 1995.