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# Absolute primes

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Absolute primes in a given base ${\displaystyle b}$ are prime numbers which are still prime numbers after any permutation whatsoever of their base ${\displaystyle b}$ digits. The base ${\displaystyle b}$ repunit primes are a subset of the base ${\displaystyle b}$ absolute primes. The base ${\displaystyle b}$ absolute primes are in turn a subset of the permutable primes.

Obviously only Mersenne primes, being binary repuntis, can be absolute primes in binary. The known decimal (base 10) absolute primes are 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97, 113, 131, 199, 311, 337, 373, 733, 919, 991 and five repunit primes (see A003459).