233 is an
irregular prime, a
full reptend prime, a
cousin prime, a
Chen prime, a
Fibonacci prime and a
sexy prime. It is the 13th
Fibonacci number. It is an
Eisenstein prime of the form
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 the 13th
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.