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223 (number)

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223 (number)

222 223 224
Cardinal two hundred twenty-three
Ordinal 223rd
(two hundred and twenty-third)
Factorization 223
Prime yes
Roman numeral CCXXIII
Binary 110111112
Ternary 220213
Quaternary 31334
Quinary 13435
Senary 10116
Octal 3378
Duodecimal 16712
Hexadecimal DF16
Vigesimal B320
Base 36 6736

223 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]

References

  1. ^ "Sloane's A000040 : The prime numbers", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^ "Sloane's A046931 : Prime islands", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^ "Sloane's A006932 : Number of permutations of [n with at least one strong fixed point]", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^ "Sloane's 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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