An emirp is a prime number

Prime number

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...

 that results in a different prime when its digits

Numerical digit

A digit is a symbol used in combinations to represent numbers in positional numeral systems. The name "digit" comes from the fact that the 10 digits of the hands correspond to the 10 symbols of the common base 10 number system, i.e...

 are reversed. This definition excludes the related palindromic prime

Palindromic prime

A palindromic prime is a prime number that is also a palindromic number. Palindromicity depends on the base of the numbering system and its writing conventions, while primality is independent of such concerns...

s. Emirps are also called reversible primes.

The sequence of emirps begins 13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157... .

All non-palindromic permutable prime

Permutable prime

A permutable prime is a prime number, which, in a given base, can have its digits' positions switched through any permutation and still spell a prime number. H. E...

s are emirps.

, 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 semiprime

Semiprime

In mathematics, a semiprime is a natural number that is the product of two prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26, ... ....

s in a similar way. That is, an emirpimes is a semiprime that is also a (distinct) semiprime upon reversing its digits.