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#proofinatoot — Public Fediverse posts

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  1. A short little episode of #CountingSheep last night:

    A palindrome number (e.g 456654) with an even number of digits cannot be prime.

    Such a \(2n\)-digit number is
    \[
    a = \sum_{k=0}^{n-1} a_k (10^k + 10^{2n-1 -k}).
    \]
    Since \(10 \equiv -1 \pmod {11}\) and the parity of the exponents of each term of the sum is opposite, we have
    \[
    a \equiv \sum_{k=0}^{n-1} a_k (1 - 1) \equiv 0 \pmod{11}
    \]
    or in other words, \(11|a\), so it's not prime.

    #ProofInAToot