An emirp (prime spelled backwards) is a prime number that results in a different prime when its digits are reversed. This definition excludes the related palindromic primes. The term reversible prime may be used to mean the same as emirp, but may also, ambiguously, include the palindromic primes.
All non-palindromic permutable primes are emirps.
The term 'emirpimes' (singular) is used also in places to treat semiprimes in a similar way. That is, an emirpimes is a semiprime that is also a (distinct) semiprime upon reversing its digits.
Emirps with added mirror properties
There is a subset of emirps x, with mirror xm, such that x is the yth prime, and xm is the ymth prime. (E.g. 73 is the 21st prime number; its mirror, 37, is the 12th prime number; 12 is the mirror of 21.
- Weisstein, Eric W., "Emirp", MathWorld.
- Rivera, Carlos. "Problems & Puzzles: Puzzle 20.- Reversible Primes". Retrieved on December 17, 2007.
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