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From: FtG@rochester.UUCP (Gary L. Peterson)
Newsgroups: net.math
Subject: Re: palindromic prime numbers -- a curious query
Message-ID: <3421@rochester.UUCP>
Date: Wed, 14-Nov-84 14:23:03 EST
Article-I.D.: rocheste.3421
Posted: Wed Nov 14 14:23:03 1984
Date-Received: Sat, 17-Nov-84 07:57:35 EST
References: <3470@ecsvax.UUCP>
Organization: U. of Rochester, CS Dept.
Lines: 16

ecsvax!unbent asks if prime palindromes must have prime length.
The following shows that the length cannot be even:

Fact 1: all numbers of the form 10**odd + 1 are divisible by 11.
Fact 2: all even length palindromes are of the form
    a1 (10**k + 1) + a2 * (10**(k-2) + 1) * 10 + ... a(k/2+1) *11 * 10**k/2
Where k = length -1 (= odd) and ai's are digits 0..9 with a1<>0.
Since each term is divisible by 11, the whole number is.

Generalization: Any even length palindrome number in base b is divisible
by b+1.

Next week: odd numbers!

FtG@rochester
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