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 nth 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 2p - 1 are all of the form 2kp + 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]

(There are 8 curios for this number that have not yet been approved by an editor.)

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