According to the Mathews page, all repunit primes (primes consisting of the digit "1" only) are rotational primes -- and that there are conjectured to be an infinite number of them.

If so, there are an infinite number of (trivial) repunit rotational primes, but there may not be any more nontrivial ones.

In reply to Re^2: Rotationally Prime Numbers Revisited by tall_man
in thread Rotationally Prime Numbers Revisited by Limbic~Region

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