Permutable prime
A permutable prime is a prime number, which, in a given base, can have its digits switched to any possible permutation and still spell a prime number. In base 10, the first few permutable primes are (with the permutations listed in parentheses)
2, 3, 5, 7, 11, 13(31), 17(71), 37(73), 79(97), 113(131, 311), 199(919, 991), 337(373, 733)
Any repunit prime can automatically be assumed to be a permutable prime as well. In base 2, only repunits can be permutable primes, because any 0 permuted to the one's place results in an even number; unless we consider 1 a prime number and 10 permutable with 01. The generalization can safely be made that for any number system based on an even number (such as decimal and sexagesimal), permutable primes can only digits that are individually odd, for any even digit permuted to the one's place results in a number divisible by two.
Referenced By
List of mathematical topics (P-R) | List of number theory topics
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