# 1091

This number is a prime. n6 + 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 pn^2 + 2pn 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]

(There are 2 curios for this number that have not yet been approved by an editor.)