View source for Emirp

{{Short description|Class of prime numbers}}
An '''emirp''' (an [[anadrome]] of ''prime'') is a [[prime number]] that results in a different prime when its decimal [[Numerical digit|digits]] are reversed.<ref name="mathworld">{{MathWorld|title=Emirp|urlname=Emirp}}</ref> This definition excludes the related [[palindromic prime]]s. The term '''''reversible prime''''' is 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, ... {{OEIS|id=A006567}}.<ref name="mathworld" />

The difference in all pairs of emirps is always a multiple of 18. This follows from all primes bigger than 2 being odd (making their differences even, i.e. multiples of 2) and from differences between pairs of natural numbers with reversed digits being multiples of 9 (which itself is a consequence of <math>10^n-1</math> being a multiple of 9 for every non-negative integer <math>n</math>).

All non-palindromic [[permutable prime]]s are emirps.

It is an open problem whether there are infinitely many emirps.

== References ==
<references/>

{{Prime number classes}}
[[Category:Classes of prime numbers]]
[[Category:Base-dependent integer sequences]]

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