223
This number is a prime.
223 is the least positive integer requiring maximum number of terms when expressed as a sum of positive 5-th powers. What is the maximum number of terms? Hint: It's an emirp.
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]
The 223rd Sophie Germain prime (12041) + 1 is divisible by
223. [Gaydos]
The sum of the first 223 distinct-digit numbers is divisible by the 223rd distinct-digit number. [Gaydos]
The expression 2^x + 2^x + 3^x is prime for x = 0 thru 6. [Anitha]
German astronomer Johannes Kepler composed 223 footnotes to his novel Somnium—several times longer than the actual text. [Edward]
The only prime whose reversal divided by its sum of its digits concatenated is the same prime. [Sariyar]
In the treatise "Measurement of a Circle" by Archimedes, Proposition 3 states: The ratio of the circumference of any
circle to its diameter is greater than 223/71 (where both numerator & denominator are prime), but less than 22/7. [Prisacariu]
The smallest odd prime containing more even digits than odd
digits. [Nie]