233, or 11101001 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.
