Emirp
Class of prime numbers
An emirp (prime spelled backwards) is a prime number that results in a different prime when its decimal digits are reversed.[1] This definition excludes the related palindromic primes. 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, ... (sequence A006567 in the OEIS).[1]
The difference in all pairs of emirps is always a multiple of 18.
All non-palindromic permutable primes are emirps.
It is an open problem whether there are infinitely many emirps.
References
- ^ a b Weisstein, Eric W. "Emirp". MathWorld.
- v
- t
- e
Prime number classes
- Fermat (22n + 1)
- Mersenne (2p − 1)
- Double Mersenne (22p−1 − 1)
- Wagstaff (2p + 1)/3
- Proth (k·2n + 1)
- Factorial (n! ± 1)
- Primorial (pn# ± 1)
- Euclid (pn# + 1)
- Pythagorean (4n + 1)
- Pierpont (2m·3n + 1)
- Quartan (x4 + y4)
- Solinas (2m ± 2n ± 1)
- Cullen (n·2n + 1)
- Woodall (n·2n − 1)
- Cuban (x3 − y3)/(x − y)
- Leyland (xy + yx)
- Thabit (3·2n − 1)
- Williams ((b−1)·bn − 1)
- Mills (⌊A3n⌋)
- Fibonacci
- Lucas
- Pell
- Newman–Shanks–Williams
- Perrin
- Palindromic
- Emirp
- Repunit (10n − 1)/9
- Permutable
- Circular
- Truncatable
- Minimal
- Delicate
- Primeval
- Full reptend
- Unique
- Happy
- Self
- Smarandache–Wellin
- Strobogrammatic
- Dihedral
- Tetradic
- Twin (p, p + 2)
- Bi-twin chain (n ± 1, 2n ± 1, 4n ± 1, …)
- Triplet (p, p + 2 or p + 4, p + 6)
- Quadruplet (p, p + 2, p + 6, p + 8)
- k-tuple
- Cousin (p, p + 4)
- Sexy (p, p + 6)
- Chen
- Sophie Germain/Safe (p, 2p + 1)
- Cunningham (p, 2p ± 1, 4p ± 3, 8p ± 7, ...)
- Arithmetic progression (p + a·n, n = 0, 1, 2, 3, ...)
- Balanced (consecutive p − n, p, p + n)
 | This article about a number is a stub. You can help Wikipedia by expanding it. |
- v
- t
- e
