User:Infovarius/Circular prime

Circular prime Circular prime is the prime which remain prime on any cyclic rotation of their digits. Because this property clearly depends on the radix in which we write the numbers sometimes they define more precisely as decimal circular primes.

Any one digit prime is circular by default. In base ten, any circular prime with two or more digits can only contain the digits 1, 3, 7 and 9. Otherwise when we rotate a 0, 2, 4, 5, 6, or 8 into the units place, the result will be divisible by 2 or 5.

Example
1193, 1931, 9311 and 3119 are all primes and so they are all circular primes.

All known circular primes
List all the known circular primes by just listing the smallest representative from each cycle, that is, we list just 1193, not 1193, 1931, 9311 and 3119: 2, 3, 5, 7, 11, 13, 17, 37, 79, 113, 197, 199, 337, 1193, 3779, 11939, 19937, 193939, 199933, R19, R23, R317, R1031 and possibly R49081

These last five are the known repunit primes and probable-prime.

Finiteness of the subject
Until 2006 it was unknown whether the quantity of circular primes is finite or infinite. But there are strong belief that it is infinite.

It is conjectured that there are infinitely many repunit primes, so there should be infinitely many circular primes. But it is highly likely that all circular primes not on the list above are repunits.

Links

 * Table of all known circular primes (current status)
 * Circular Prime article In Prime pages glossary