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From: unbent@ecsvax.UUCP
Newsgroups: net.math
Subject: palindromic prime numbers -- a curious query
Message-ID: <3470@ecsvax.UUCP>
Date: Tue, 13-Nov-84 15:30:33 EST
Article-I.D.: ecsvax.3470
Posted: Tue Nov 13 15:30:33 1984
Date-Received: Thu, 15-Nov-84 02:17:39 EST
Lines: 26

==>
	My colleague, Paul Ziff, is a collector of both patterns and prime
numbers.  Recently these two avocations intersected in his noticing
*palindromic primes*, i.e., primes whose decimal representations read the
same forward and backward:  11, 101, 151, 757, for example.  He fired up
his little house computer and set off in search of them.  Evidently he came
up with quite a few, before running out of computational ability.  In the
process, he noticed something else:  There weren't any 4-digit, 6-digit, or
8-digit palindromic primes.  Maybe he got beyond that, to 9- and/or 10-digit
primes, because he got far enough, in any event, to arrive at a conjecture:

Ziff's conjecture:  The number of digits in the decimal representation of a
palindromic prime is itself prime.

He asked me if I had any idea (1) whether anything like that conjecture was
known to be true, and (2) how in the world one might go about trying to
establish a strange conjecture like that.  [It's strange because it attempts
to interrelate facts about *numbers* with facts about (decimal) *numerals*.]
I didn't know the answer to either (1) or (2), but I told him I'd put it on
the net -- and here it is.  Anyone out there have any ideas?


		    	          --Jay Rosenberg
				    Dept. of Philosophy
...mcnc!ecsvax!unbent		    Univ. of North Carolina
				    Chapel Hill, NC  27514