121 (number)

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121 is the natural number following 120 and preceding 122.

Cardinal One hundred [and]
twenty-one
Ordinal 121st
Factorization 112
Roman numeral CXXI
Binary 1111001
Hexadecimal 79

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[edit] In mathematics

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 + p2 + p3 + p4, 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.

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. But it can not be expressed as the sum of any other number plus that number's digits, making 121 a self number.

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121 is also:

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[edit] References

  1. ^ Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 136