# 1091

This number is a prime.

*n*^{6} + 1091 is composite for all values of *n* from 1 to 3905. [Shanks]

The smallest Honaker emirp. Note that its next Honaker prime (1301) is also an emirp and the concatenation of these two emirps (13011091) is prime as well. [Loungrides]

The first occurrence of a sexy quadruplet (*p*,
*p* + 6, *p* + 12, *p* + 18) of consecutive
emirps: (1091, 1097, 1103, 1109). Note that the end terms
are consecutive invertible primes whose digits are mere
cyclic permutations of each other. [Beedassy]

The only known invertible emirp of form (x^3+y^3+z^3)/(x+y+z), where x, y, z are consecutive numbers (case x=32), i.e., 1091=(32^3+33^3+34^3)/(32+33+34). [Loungrides]

The smallest prime obtained by writing before a composite number the sum of its digits. [Silva]

The first prime of the form p_{n^2} +
2p_{n} which also has an index equal to n^2 + n
(case n=13). [Barnes]

The smaller prime (emirp) in the first pair of invertible primes, (1091, 1601), whose concatenation, i.e., 10911601, is a strobogrammatic prime. [Loungrides]

The smallest Honaker bemirp. [Hensley]

The smallest Honaker prime that falls between two happy numbers. [Gaydos]

The smallest prime number whose square (1190281) is an anagram of the prime and its prime index (182). [Gaydos]

The smallest Honaker prime that becomes a Sophie Germain prime when turned upside down. [Jha]

1091 divides the concatenation of first sixty-one bemirps. [Sariyar]