en 223 (number)

← 222 223 224 →
← 220 221 222 223 224 225 226 227 228 229 → List of numbers; Integers; ← 0 100 200 300 400 500 600 700 800 900 →
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.

In mathematics

223 is:

a prime number,^[1]
a lucky prime,^[2]
a left-truncatable prime,^[3] and a left-and-right-truncatable prime.^[4]

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.^[5]

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.^[6]

In other fields

.223 (disambiguation), the caliber of several firearm cartridges
The years 223 and 223 BC
The number of synodic months of a Saros

References

^ Sloane, N. J. A. (ed.). "Sequence A000040 (The prime numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A031157 (Numbers that are both lucky and prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A024770 (Right-truncatable primes: every prefix is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A077390 (Primes which leave primes at every step if most significant digit and least significant digit are deleted until a one digit or two digit prime is obtained)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^ 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.
^ 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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[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 A031157 (Numbers that are both lucky and prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

[3] Sloane, N. J. A. (ed.). "Sequence A024770 (Right-truncatable primes: every prefix is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

[4] Sloane, N. J. A. (ed.). "Sequence A077390 (Primes which leave primes at every step if most significant digit and least significant digit are deleted until a one digit or two digit prime is obtained)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

[5] 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.

[6] 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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