I know what 23 is as well
Twenty-three is the ninth
prime number, the smallest odd prime which is not a
twin prime. Twenty-three is also the fifth
factorial prime, the second
Woodall prime. It is an
Eisenstein prime with no
imaginary part and
real part of the form
3n − 1.
The fifth
Sophie Germain prime and the fourth
safe prime, 23 is the next to last member of the first
Cunningham chain of the first kind to have five terms (2, 5, 11, 23, 47). Since 14! + 1 is a multiple of 23 but 23 is not one more than a multiple 14, 23 is a
Pillai prime. 23 is the smallest odd prime to be a
highly cototient number, as the solution to
x - φ(
x) for the integers 95, 119, 143, 529.
Twenty-three is the
aliquot sum of two
integers; the discrete
biprimes 57 and
85 and is the base of the 23-aliquot tree.
23 is the first prime
P for which unique factorization of cyclotomic integers based on the
P'th root of unity breaks down.
The sum of the first 23 primes is 874, which is divisible by 23, a property shared by few other numbers.
[1][2]
In the list of
Fortunate numbers, 23 occurs twice, since adding 23 to either the fifth or eighth
primorial gives a prime number (namely 2333 and 9699713).
23 also has the distinction of being one of two integers that cannot be expressed as the sum of fewer than 9 cubes of integers (the other is
239). See
Waring's problem.
23 is a
Wedderburn-Etherington number. The codewords in the perfect (non-extended)
binary Golay code are of size 23.
According to the
birthday paradox, in a group of 23 (or more) randomly chosen people, the probability is more than 50% that some pair of them will have the same birthday.
There were 23 problems on
David Hilbert's famous list of unsolved mathematical problems, presented to the
International Congress of Mathematicians in Paris in 1900.
In base 10, 23 is the second
Smarandache-Wellin prime, as it is the concatenation of the base 10 representations of the first two primes (2 and 3) and is itself also prime. It is also a
happy number in base 10. 23
! is 23 digits long in base 10. There are only three other numbers that have this property: 1, 22, and 24.
The
natural logarithms of all
positive integers lower than 23 are known to have binary
BBP-type formulae.
[3]
The first 6 digits of
Pi are 3.14159 which all add up to 23.
Take THAT Disney23.
-dave