# 223

This number is a prime.

The largest prime which cannot be represented with less than 37 5th powers.

The number of primes and the number of composites that cannot be written as the sum of two primes, up to 223, are equal. [Honaker]

The sums of the *n*th powers of its digits are prime for all *n* between 1 and 6 inclusive: sum of digits = 7, sum of squares of digits = 17, sum of cubes of digits = 43, sum of fourth powers = 113, sum of fifth powers = 307 and sum of sixth powers = 857. [Trotter]

One Saros cycle is almost exactly 223 synodic months.

Prime in the decimal expansion of square root of 5. [Haga]

A chicken and human have 223 enzymes of identical sequence length. [Jolly]

The prime factors of 2^{p} - 1 are all of the form
2*k**p* + 1, where *k* is a positive integer, and *p*
is an odd prime. Fermat used this fact to show that 223 divides the Mersenne number *M*(37).

A prime extracted from the names of the most famous Star Wars droids, i.e., R2-D2 and C-3PO. May the Force of Prime Numbers be with you! [Capelle]

The sum of the digits of first primes up to 223 is 449. Note the prime digits and their squares. [Silva]

The smallest prime showing a repeated prime digit. [Silva]

The smallest prime whose reversal has more than two prime divisors. [Silva]

The largest gear in the Antikythera mechanism most likely had 223 teeth in connection with the prediction of lunar eclipses. [Beedassy]

The smallest prime formed from three prime digits. [Silva]

223 = -01+23+45+67+89. [Silva]

The smallest prime that has more primitive roots below p/2 than above p/2. [Gudipati]

"The children of Hashum, **two hundred twenty and three**." (*Ezra*
2:19, KJV) [Dorton]

(223, 227, 229, 233) is the first tetrad of successive primes whose the digits of each prime are complementary of the digits of another tetrad of successive primes, i.e., (887, 883, 881, 877). [Loungrides]

The only 3-digit isolated prime concatenated from two isolated primes, 2 and 23. [Loungrides]

ß was encoded by ECMA at position 223 (hexadecimal DF). [Hess]

223 is the first of 13 consecutive primes squared having squares as the last three digits. [Bergot]

The first Carol prime, i.e., a prime of form (2^x-1)^2-2, for x a composite, (x=4). Note that 223 is a prime-digit prime. [Loungrides]

The starting prime of a sequence of five primes following this rule: The Kth prime is obtained from the previous one substituting each digit d by d^K: 223, 449, 6464729, 129625612962562401166561, 1325904977763231257776132590497776323125777632102401177767776312577761. [Rivera]