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A question on palindromic primes

  1. Sep 21, 2014 #1

    Char. Limit

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    So just for fun, I decided to look for a list of palindromic primes, that is, primes that when in base 10 representation are the same whether backward or forward. 1003001, just to give an example. I quickly noticed something striking: Other than 11, every palindromic prime out of the first 100,000 primes had an odd number of digits! Naturally, I wondered just why this was, but not being a number theorist, I cannot for the life of me figure out why without help.

    So with that, I must ask: Can you help me understand just why 4 and 6 digit palindromic numbers, as a rule, are composite? Does a reason even exist in the first place? And finally, can a proof be made to show that 11 is the only even-digited palindromic prime?
  2. jcsd
  3. Sep 21, 2014 #2


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    Staff: Mentor

  4. Sep 21, 2014 #3

    Char. Limit

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    Haha, whoops. Shame on me indeed. If I'm allowed an excuse, I'd like to put forth the one that says I'm on mobile.
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