# Definition:Permutable Prime

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## Definition

A **permutable prime** is a prime number $p$ which has the property that all anagrams of $p$ are prime.

### Sequence

The sequence of **permutable primes** begins:

- $2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97, 113, 131, 199, 311, 337, 373, 733, 919, 991, R_{19}, R_{23}, R_{317}, R_{1091}, \ldots$

where $R_n$ denotes the repunit of $n$ digits.

The smallest
elements of the permutation sets of these are:

- $2, 3, 5, 7, 11, 13, 17, 37, 79, 113, 199, 337, R_{19}, R_{23}, R_{317}, R_{1091}, \ldots$

## Also defined as

Some sources insist that a **permutable prime** must have at least $2$ distinct digits, which excludes the trivial cases of the $1$-digit primes and repunits:

- $13, 17, 31, 37, 71, 73, 79, 97, 113, 131, 199, 311, 337, 373, 733, 919, 991$

This sequence is A129338 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

## Also known as

A **permutable prime** can also be referred to as an **absolute prime**.

The author of this webpage, before learning what its actual name is, toyed with the idea of coining the term **permi**, inspired by the term **emirp**.

## Also see

- Results about
**permutable primes**can be found here.