← 222 223 224 →
Cardinaltwo hundred twenty-three
Ordinal223rd
(two hundred twenty-third)
Factorizationprime
PrimeYes
Greek numeralΣΚΓ´
Roman numeralCCXXIII
Binary110111112
Ternary220213
Senary10116
Octal3378
Duodecimal16712
HexadecimalDF16

223 (two hundred [and] twenty-three) is the natural number following 222 and preceding 224.

In mathematics

223 is a prime number.[1] Among the 720 permutations 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.[2]

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.[3]

In other fields

References

  1. ^ Sloane, N. J. A. (ed.). "Sequence A000040 (The prime numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^ Sloane, N. J. A. (ed.). "Sequence A006932 (Number of permutations of [n] with at least one strong fixed point)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^ Sloane, N. J. A. (ed.). "Sequence A048267 (Largest integer requiring n fifth powers to sum to it, starting with n=28)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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