dihedral prime

A dihedral primeMathworldPlanetmath or dihedral calculator prime is a prime numberMathworldPlanetmath that still reads like itself or another prime number when read in a seven-segment display, regardless of orientation (normally or upside down), and surface (actual display or reflectionMathworldPlanetmath on a mirror). The first few base 10 dihedral primes are 2, 11, 101, 181, 1181, 1811, 18181, 108881, 110881, 118081, 120121, 121021, 121151, 150151, 151051, 151121, 180181, 180811, 181081, etc. These are listed in A038136 of Sloane’s OEIS.

The smallest dihedral prime that reads differently with each orientation and surface combinationMathworldPlanetmath is 120121.

The digits 0, 1 and 8 remain the same regardless of orientation or surface. 2 and 5 turn into each other when viewed upside down or reflected on a mirror. In the display of a scientific calculator that can handle hexadecimal, 3 would become E reflected, but E being an even digit, the 3 can’t be used as the first digit because the reflected number will be even. Though 6 and 9 become each other upside down, they are not valid digits when reflected, at least not in any of the numeral systems pocket calculators usually operate in. In binary, all palindromic primesMathworldPlanetmath are dihedral.

Strobogrammatic primes that don’t use 6 or 9 are dihedral primes.

Title dihedral prime
Canonical name DihedralPrime
Date of creation 2013-03-22 16:46:53
Last modified on 2013-03-22 16:46:53
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 4
Author PrimeFan (13766)
Entry type Definition
Classification msc 11A63
Synonym dihedral calculator prime