Permutable Prime Number : Means with Examples (original) (raw)

Last Updated : 23 Jul, 2025

Permutable Prime is also known as full Prime, Absolute Prime, or Anagrammatic Prime. A Permutable prime is a prime number that remains prime even with rearranging of its digits in any particular order. All possible permutation of permutable prime are also prime number.

It seems similar to circular prime but in circular prime only cyclic permutation needs to be prime, but here all possible permutation are prime. For example, take the number 113. It's a prime number, and if we rearrange its digits in all possible ways, we get:

113 → 131 (prime)
113 → 311 (prime)

Since all the permutations of 113 result in prime numbers, 113 is a permutable prime.

Examples of Permutable Prime

Here are some examples:

**13 – The digits can be rearranged as 13 or 31, both of which are prime numbers.
**17 – The digits can be rearranged as 17 or 71, both of which are primes.
**37 – The digits can be rearranged as 37 or 73, both of which are primes.
**79 – The digits can be rearranged as 79 or 97, both of which are primes.
**113 – The digits can be rearranged as 113, 131, or 311, all of which are primes.

First few permutable primes are:

2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97, 113, 131, 199, 311, 337, 373, 733, 919, 991, 1111111111111111111, 11111111111111111111111, . . .

**Note: All repunit primes are permutable primes.

Largest Permutable Prime

As repunit primes are also permutable, thus the largest repunit prime is also the largest known permutable prime as well i.e., R8177207 = (108177207-1)/9 = 111… (8177207 ones) …111.

Conclusion

In conclusion, **permutable primes are a unique type of prime numbers that stay prime even when their digits are rearranged. These rare primes remind us of the surprising patterns that can be found in mathematics.

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