the sum of the powers of 3 from 0 to 4, so a
repunit in
ternary. Furthermore, 121 is the only square of the form , where p is prime (3, in this case).[1]
the sum of three consecutive
prime numbers (37 + 41 + 43).
As , it provides a solution to
Brocard's problem. There are only two other squares known to be of the form . Another example of 121 being one of the few numbers supporting a conjecture is that Fermat conjectured that 4 and 121 are the only perfect squares of the form (with x being 2 and 5, respectively).[2]
In decimal, it is a
Smith number since its digits add up to the same value as its factorization (which uses the same digits) and as a consequence of that it is a
Friedman number (). But it cannot be expressed as the sum of any other number plus that number's digits, making 121 a
self number.