121 (number)

121 (one hundred [and] twenty-one) is the natural number following 120 and preceding 122.

In mathematics

One hundred [and] 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 , 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 Brocard's 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 x³ - 4 (with x being 2 and 5, respectively).^[1]

It is also a star number and a centered octagonal number.

A Chinese checkers board has 121 holes

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 number's digits, making 121 a self number.

In other fields

121 is also:

• The electricity emergency telephone number in Egypt
• The number for voicemail for mobile phones on the Vodafone network^[2]
• The undiscovered chemical element Unbiunium has the atomic number 121
• The official end score for Cribbage^[3]

See also

• List of highways numbered 121
• United States House of Representatives House Resolution 121
• United Nations Security Council Resolution 121

References

1. ↑ Wells, D., The Penguin Dictionary of Curious and Interesting Numbers, London: Penguin Group. (1987): 136
2. ↑ Vodafone, Calling and messaging
3. ↑ Rule 1.1, American Cribbage Congress, retrieved 6 September 2011