ⓘ 121 (number)

                                     

ⓘ 121 (number)

One hundred twenty-one 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