Dihedral prime
This article needs additional citations for verification. (December 2023) |
A dihedral prime or dihedral calculator prime is a prime number 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 reflection on a mirror). The first few decimal dihedral primes are
- ).
The smallest dihedral prime that reads differently with each orientation and surface combination is 120121 which becomes 121021 (upside down), 151051 (mirrored), and 150151 (both upside down and mirrored).
The digits 0, 1 and 8 remain the same regardless of orientation or surface (the fact that 1 moves from the right to the left of the seven-segment cell when reversed is ignored). 2 and 5 remain the same when viewed upside down, and turn into each other when reflected in a mirror. In the display of a calculator that can handle
The palindromic prime 10180054 + 8×(1058567−1)/9×1060744 + 1, discovered in 2009 by Darren Bedwell, is 180,055 digits long and may be the largest known dihedral prime as of 2009[update].[1]
See also
- Strobogrammatic prime
Notes
- ^ Chris Caldwell, The Top Twenty: Palindrome. Retrieved on 2009-09-16
References
- Mike Keith. "Puzzle 39.- The Mirrorable Numbers". The prime puzzles & problems connection.
- Eric W. Weisstein. "Dihedral Prime". MathWorld – A Wolfram Web Resource.