223 (two hundred
ndtwenty-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
222
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Year 222 ( CCXXII) was a common year starting on Tuesday of the Julian calendar. In the Roman Empire, it was known as the Year of the Consulship of Antoninus and Severus (or, less frequently, year 975 ''Ab urbe condita''). The denomi ...
and preceding
224.
In mathematics
223 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 ...
,
*a
lucky prime,
*a left-
truncatable prime, and a
left-and-right-truncatable prime.
Among the 720
permutation
In mathematics, a permutation of a set can mean one of two different things:
* an arrangement of its members in a sequence or linear order, or
* the act or process of changing the linear order of an ordered set.
An example of the first mean ...
s of the numbers from 1 to 6, exactly 223 of them have the property that at least one of the numbers is fixed in place by the permutation and the numbers less than it and greater than it are separately permuted among themselves.
In connection with
Waring's problem, 223 requires the maximum number of terms (37 terms) when expressed as a sum of positive fifth powers, and is the only number that requires that many terms.
See also
* The years
223 and
223 BC
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Year 223 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Flaminius and Philus (or, less frequently, year 531 ''Ab urbe condita''). The denomination 223 BC for this year has bee ...
References
Integers
{{Num-stub