223 (number)

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← 222 223 224 →
Cardinal two hundred twenty-three
Ordinal 223rd
(two hundred twenty-third)
Factorization prime
Prime 48th
Greek numeral ΣΚΓ´
Roman numeral CCXXIII
Binary 110111112
Ternary 220213
Senary 10116
Octal 3378
Duodecimal 16712
Hexadecimal DF16

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

Contents

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

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References

  1. ↑ Sloane, N. J. A. (ed.). "SequenceA000040(The prime numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  2. ↑ Sloane, N. J. A. (ed.). "SequenceA006932(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.). "SequenceA048267(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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