Emirp

An emirp (prime spelled backwards) is a prime number that results in a different prime when its decimal 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.

The sequence of emirps begins 13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157, 167, 179, 199, 311, 337, 347, 359, 389, 701, 709, 733, 739, 743, 751, 761, 769, 907, 937, 941, 953, 967, 971, 983, 991, ... (sequence in the OEIS).

All non-palindromic permutable primes are emirps.

As of November 2009^[update], the largest known emirp is 10¹⁰⁰⁰⁶+941992101×10⁴⁹⁹⁹+1, found by Jens Kruse Andersen in October 2007.

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.

The emirps in base 12 are (using reversed two and three for ten and eleven, respectively)

There is a subset of emirps x, with mirror x_m, such that x is the yth prime, and x_m is the y_mth prime. (E.g. 73 is the 21st prime number; its mirror, 37, is the 12th prime number; 12 is the mirror of 21.)

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