223 (two hundred ndtwenty-three) is the

natural number In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''Cardinal n ...

following

222 __NOTOC__ Year 222 ( CCXXII) was a common year starting on Tuesday (link will display the full calendar) of the Julian calendar. In the Roman Empire, it was known as the Year of the Consulship of Antoninus and Severus (or, less frequently, ye ...

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 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 ...

. Among the 720

permutation In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or proc ...

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 In number theory, Waring's problem asks whether each natural number ''k'' has an associated positive integer ''s'' such that every natural number is the sum of at most ''s'' natural numbers raised to the power ''k''. For example, every natural num ...

, 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.

In other fields

* .223 (disambiguation), the caliber of several firearm cartridges * The years 223 and

223 BC __NOTOC__ 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 Flaminus and Philus (or, less frequently, year 531 '' Ab urbe condita''). The denomination 223 BC for this year has bee ...

* The number of synodic months of a Saros

References

Integers {{Num-stub