NationMaster - Encyclopedia: Permutable prime

A permutable prime (sometimes called a primutation) 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): In mathematics, a prime number (or prime) is a natural number greater than one whose only positive divisors are one and itself. ... // Mathematics In mathematics, especially in abstract algebra and related areas, a permutation is a bijection from a finite set X onto itself. ...

2, 3, 5, 7, 11, 13(31), 17(71), 37(73), 79(97), 113(131, 311), 199(919, 991), 337(373, 733) 2 (two) is a number, numeral, and glyph. ... 3 (three) is a number, numeral, and glyph. ... 5 (five) is a number, numeral, and glyph. ... This article is about the number seven. ... 11 (eleven) is the natural number following 10 and preceding 12. ... See also Thirteen, a 2003 movie, 13 an album by British band Blur, Thirteen an album by Teenage Fanclub. ... 31 (thirty-one) is the natural number following 30 and preceding 32. ... 17 (seventeen) is the natural number following 16 and preceding 18. ... 71 is the natural number following 70 and preceding 72. ... 37 is the natural number following 36 and preceding 38. ... 73 is the natural number following 72 and preceding 74. ... 79 is the natural number following 78 and preceding 80. ... 97 is the natural number following 96 and preceding 98. ... 113 is the natural number following 112 and preceding 114. ... 131 is the natural number following 130 and preceding 132. ... 199 is the natural number between 198 and 200. ...

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 have digits that are individually odd, for any even digit permuted to the one's place results in a number divisible by two. In recreational mathematics, a repunit is a number like 11, 111, or 1111 that contains only the digit 1. ...

External link

Sloane's A003459

Category: Prime numbers

Results from FactBites:

Permutation - encyclopedia article about Permutation. (2980 words)
	A permutation is an ordered sequence containing each symbol from a set once and only once; neither "1, 2, 2, 3, 4, 5, 6" nor "1, 2, 4, 5, 6" are permutations.
	An even permutation is a permutation which can be expressed as the product of an even number of transpositions, and the identity permutation is an even permutation as it equals (1 2)(1 2).
	In mathematics, a permutation group is a group G whose elements are permutations of a given set M, and whose group operation is the composition of permutations in G (which are thought of as bijective functions from the set M to itself); the relationship is often written as (G,M).

User:PrimeFan - Wikipedia, the free encyclopedia (928 words)
	I'm fascinated by repunit primes in various bases while simultaneously feeling a bit guilty about devoting too much time to kinds of primes that are base-dependent, such as Smarandache-Wellin primes.
	So far the only primes I know of this form are 2 (which is a consequence of the algebraic definition, not the base-dependend one), 11 and 101.
	The primes less than 41 that meet this criterion are 3, 5, 7, 11 and 17.

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