#proofinatoot — Public Fediverse posts
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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.