223 (number)

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← 222 223 224 →
Cardinaltwo hundred twenty-three
Ordinal223rd
(two hundred twenty-third)
Factorizationprime
PrimeYes
Greek numeralΣΚΓ´
Roman numeralCCXXIII
Binary110111112
Ternary220213
Quaternary31334
Quinary13435
Senary10116
Octal3378
Duodecimal16712
HexadecimalDF16
VigesimalB320
Base 366736

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

223 is a prime number.[1] It is the smallest prime for which the two nearest primes on either side of it are 16 units apart.[2] 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.[3]

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.[4]

In other fields[edit]

References[edit]

  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 A046931 (Prime islands)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^ 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.
  4. ^ 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.