ⓘ 121 (number)
One hundred twentyone is a square and is the sum of three consecutive primes 37 + 41 + 43. There are no squares besides 121 known to be of the form 1 + p + p 2 + p 3 + p 4 {\displaystyle 1+p+p^{2}+p^{3}+p^{4}}, where p is prime 3, in this case. Other such squares must have at least 35 digits.
There are only two other squares known to be of the form n! + 1, supporting Brocards conjecture. Another example of 121 being of the few examples supporting a conjecture is that Fermat conjectured that 4 and 121 are the only perfect squares of the form x 3  4 with x being 2 and 5, respectively.
It is also a star number and a centered octagonal number.
In base 10, 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 11^2. But it can not be expressed as the sum of any other number plus that numbers digits, making 121 a self number.
1. In other fields
121 is also:
 The undiscovered chemical element Unbiunium has the atomic number 121
 The number for voicemail for mobile phones on the Vodafone network
 The electricity emergency telephone number in Egypt
 The official end score for Cribbage

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