Let $Y(k)$ be the number consisting of $1$, repeated $k$ times. We know that $Y(2) =11$ is prime. It so happens that $Y(19)$ and $Y(23)$ are also prime.
Are there any more?
Regards,
David
2026-02-23 06:34:50.1771828490
Primes with digits only 1
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To summarize the comments, the repunit $$Y(k)=\frac{10^k-1}9,$$ the number $11...111$ consisting of $k$ copies of the digit $1,$ is known to be prime for
$k=2, 19, 23, 317,$ and $1031.$
Source: The On-Line Encyclopedia of Integer Sequences.