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- Permutable_prime abstract "A permutable prime is a prime number which, in a given base, can have its digits' positions switched through any permutation and still be a prime number. H. E. Richert, who is supposed to be the first to study these primes, called them permutable primes, but later they were also called absolute primes.In base 10, all the permutable primes with fewer than 49,081 digits are known (sequence A003459 in OEIS):2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97, 113, 131, 199, 311, 337, 373, 733, 919, 991, R19 (1111111111111111111), R23, R317, R1031.Of the above, there are 16 unique permutation sets, with smallest elements2, 3, 5, 7, R2, 13, 17, 37, 79, 113, 199, 337, R19, R23, R317, R1031.Note Rn = is a repunit, a number consisting only of n ones (in base 10). Any repunit prime is a permutable prime with the above definition, but some definitions require at least two distinct digits.All permutable primes of two or more digits are composed from the digits 1, 3, 7, 9, because no prime number except 2 is even, and no prime number besides 5 is divisible by 5. It is proved that no permutable prime exists which contains three different of the four digits 1, 3, 7, 9, as well as that there exists no permutable prime composed of two or more of each of two digits selected from 1, 3, 7, 9.There is no n-digit permutable prime for 3 < n < 6·10175 which is not a repunit. It is conjectured that there are no non-repunit permutable primes other than those listed above.In base 2, only repunits can be permutable primes, because any 0 permuted to the one's place results in an even number. Therefore the base 2 permutable primes are the Mersenne primes. The generalization can safely be made that for any positional number system, permutable primes with more than one digit can only have digits that are coprime with the radix of the number system. One-digit primes, meaning any prime below the radix, are always trivially permutable.".
- Permutable_prime wikiPageID "421593".
- Permutable_prime wikiPageRevisionID "603642212".
- Permutable_prime hasPhotoCollection Permutable_prime.
- Permutable_prime subject Category:Base-dependent_integer_sequences.
- Permutable_prime subject Category:Classes_of_prime_numbers.
- Permutable_prime subject Category:Permutations.
- Permutable_prime type Abstraction100002137.
- Permutable_prime type Arrangement107938773.
- Permutable_prime type Base-dependentIntegerSequences.
- Permutable_prime type Change107296428.
- Permutable_prime type Class107997703.
- Permutable_prime type ClassesOfPrimeNumbers.
- Permutable_prime type Collection107951464.
- Permutable_prime type Event100029378.
- Permutable_prime type Group100031264.
- Permutable_prime type Happening107283608.
- Permutable_prime type Ordering108456993.
- Permutable_prime type Permutations.
- Permutable_prime type PsychologicalFeature100023100.
- Permutable_prime type Sequence108459252.
- Permutable_prime type Series108457976.
- Permutable_prime type Substitution107443761.
- Permutable_prime type Variation107337390.
- Permutable_prime type YagoPermanentlyLocatedEntity.
- Permutable_prime comment "A permutable prime is a prime number which, in a given base, can have its digits' positions switched through any permutation and still be a prime number. H. E.".
- Permutable_prime label "Nombre premier permutable".
- Permutable_prime label "Permutable prime".
- Permutable_prime label "Permutierbare Primzahl".
- Permutable_prime label "Primo permutabile".
- Permutable_prime label "可交换素数".
- Permutable_prime sameAs Permutierbare_Primzahl.
- Permutable_prime sameAs Nombre_premier_permutable.
- Permutable_prime sameAs Primo_permutabile.
- Permutable_prime sameAs 재배열_가능_소수.
- Permutable_prime sameAs m.026j9p.
- Permutable_prime sameAs Q633958.
- Permutable_prime sameAs Q633958.
- Permutable_prime sameAs Permutable_prime.
- Permutable_prime wasDerivedFrom Permutable_prime?oldid=603642212.
- Permutable_prime isPrimaryTopicOf Permutable_prime.