233 is an irregular prime, a full reptend prime, a cousin prime, a Chen prime, and a sexy prime. It is an Eisenstein prime of the form 3n − 1 with no imaginary part. Since 233 × 2 + 1 = 467, another prime, 233 is a Sophie Germain prime. 233 is also a prime triplet (with 227 and 229).
It is a Fibonacci number, being the sum of 89 and 144. Being an odd-indexed Fibonacci number, it is also a Markov number, appearing in solutions to the Markov Diophantine equation: (1, 89, 233), (89, 233, 610), (233, 610, 426389), ...
In base 10 there is no integer that added up to its own digits yields 233, hence 233 is a self number. In base 3, the sum of 233's digits is composite, no smaller prime has this property.
Note: I have NO idea what most of this means but isn't there a lot?
In other fields
In current teenage slang and Internet discourse, 233 is sometimes used instead of BFF to abbreviate "Best Friends Forever." The digits correspond to the number keys that would be pressed on a telephone while sending a text message. In Windows live messenger 233 is a commonly used to represent the emoticon of raised eybrows.
Wandering aimlessly through FT since 1999.