Permutable Prime with more than 3 Digits is Probably Repunit/Historical Note

Historical Note on Permutable Prime with more than 3 Digits is Probably Repunit
It is trivially true, as shown in Digits of Permutable Prime, that a permutable prime with more than $1$ digit can contain only the digits from the set $\set {1, 3, 7, 9}$.

and demonstrated in a $1974$ paper that a permutable prime cannot contain all of $1$, $3$, $7$ and $9$.

Subsequently, showed that a non-repunit permutable prime is of the form $\sqbrk {aaa \cdots aab}$ and have more than $9$ billion digits.

In $1995$, determined further restrictions on the structure of permutable primes.

However, it still has not been proven that a permutable prime with more than $3$ digits is always a repunit prime.