1093 is the natural number following 1092 and preceding 1094. 1093 is a

prime number A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

. Together with 1091 and 1097, it forms a

prime triplet In number theory, a prime triplet is a set of three prime numbers in which the smallest and largest of the three differ by 6. In particular, the sets must have the form or . With the exceptions of and , this is the closest possible grouping of t ...

. It is a

happy prime In number theory, a happy number is a number which eventually reaches 1 when replaced by the sum of the square of each digit. For instance, 13 is a happy number because 1^2+3^2=10, and 1^2+0^2=1. On the other hand, 4 is not a happy number because ...

and a star prime. It is also the smallest

Wieferich prime In number theory, a Wieferich prime is a prime number ''p'' such that ''p''2 divides , therefore connecting these primes with Fermat's little theorem, which states that every odd prime ''p'' divides . Wieferich primes were first described by Ar ...

. 1093 is a repunit prime in base 3 because: :

1093 = 1111111_3 = 3^6 + 3^5 + 3^4 + 3^3 + 3^2 + 3^1 + 3^0 = \frac{2} \, .

References

Die Welt der Primzahlen
p. 237

p. 240
Meine Zahlen, meine Freunde
p. 223

Number Gossip: 1093

Prime Curios!: 1093
Integers