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 (mathematics), 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 ...
. 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 ...
. It is a
happy prime
In number theory, a happy number is a number which eventually reaches 1 when the number is 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 ...
and a
star prime
In mathematics, a star number is a centered number, centered figurate number, a centered hexagram (six-pointed star), such as the Star of David, or the board Chinese checkers is played on.
The ''n''th star number is given by the formula ''Sn'' ...
. 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 A ...
. 1093 is a
repunit prime
In recreational mathematics, a repunit is a number like 11, 111, or 1111 that contains only the digit 1 — a more specific type of repdigit. The term stands for "repeated unit" and was coined in 1966 by Albert H. Beiler in his book ''Recr ...
in base 3 because:
:
References
* p. 237
* p. 240
* p. 223
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Integers
{{Num-stub