193 (one hundred
ndninety-three) is the
natural number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...
following
192 and preceding
194.
In mathematics
193 is the number of
compositions of
14 into distinct parts. In
decimal
The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers (''decimal fractions'') of th ...
, it is the seventeenth
full repetend prime, or ''long prime''.
* It is the only odd prime
known for which 2 is not a
primitive root of
.
* It is the thirteenth
Pierpont prime
In number theory, a Pierpont prime is a prime number of the form
2^u\cdot 3^v + 1\,
for some nonnegative integers and . That is, they are the prime numbers for which is 3-smooth. They are named after the mathematician James Pierpont, who us ...
, which implies that a
regular 193-gon can be constructed using a
compass
A compass is a device that shows the cardinal directions used for navigation and geographic orientation. It commonly consists of a magnetized needle or other element, such as a compass card or compass rose, which can pivot to align itself with No ...
,
straightedge
A straightedge or straight edge is a tool used for drawing straight lines, or checking their straightness. If it has equally spaced markings along its length, it is usually called a ruler.
Straightedges are used in the automotive service and ma ...
, and
angle trisector.
* It is part of the fourteenth pair of
twin prime
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair or In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin prime' ...
s
, the seventh trio of
prime triplets
, and the fourth set of
prime quadruplets
.
Aside from itself, the ''
friendly giant'' (the largest
sporadic group) holds a total of 193
conjugacy classes.
It also holds at least 44
maximal subgroup
In mathematics, the term maximal subgroup is used to mean slightly different things in different areas of algebra.
In group theory, a maximal subgroup ''H'' of a group ''G'' is a proper subgroup, such that no proper subgroup ''K'' contains ''H'' ...
s aside from the
double cover of
(the forty-fourth prime number is 193).
193 is also the eighth
numerator of convergents to
Euler's number
The number is a mathematical constant approximately equal to 2.71828 that is the base of the natural logarithm and exponential function. It is sometimes called Euler's number, after the Swiss mathematician Leonhard Euler, though this can ...
; correct to three decimal places:
The denominator is
71, which is the largest
supersingular prime that uniquely divides the
order
Order, ORDER or Orders may refer to:
* A socio-political or established or existing order, e.g. World order, Ancien Regime, Pax Britannica
* Categorization, the process in which ideas and objects are recognized, differentiated, and understood
...
of the friendly giant.
See also
*
193 (disambiguation)
References
{{DEFAULTSORT:193 (Number)
Integers