189 (one hundred
ndeighty-nine) is the
natural number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...
following
188 and preceding
190.
In mathematics
189 is a
centered cube number and a
heptagonal number.
The centered cube numbers are the sums of two consecutive
cubes
A cube or regular hexahedron is a three-dimensional space, three-dimensional solid object in geometry, which is bounded by six congruent square (geometry), square faces, a type of polyhedron. It has twelve congruent edges and eight vertices. It i ...
, and 189 can be written as
sum of two cubes
In mathematics, the sum of two cubes is a cubed number added to another cubed number.
Factorization
Every sum of cubes may be factored according to the identity
a^3 + b^3 = (a + b)(a^2 - ab + b^2)
in elementary algebra.
Binomial numbers g ...
in two ways: and The smallest number that can be written as the sum of two positive cubes in two ways is
1729
Events
January–March
* January 8 – Frederick, the eldest son of King George II of Great Britain is made Prince of Wales at the age of 21, a few months after he comes to Britain for the first time after growing up in Hanover ...
.
The largest
prime number
A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...
that can be represented in 256-bit arithmetic is the "ultra-useful prime" used in
quasi-Monte Carlo method
In numerical analysis, the quasi-Monte Carlo method is a method for numerical integration and solving some other problems using low-discrepancy sequences (also called quasi-random sequences or sub-random sequences) to achieve variance reduction. ...
s and in some
cryptographic
Cryptography, or cryptology (from "hidden, secret"; and ''graphein'', "to write", or '' -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adversarial behavior. More gen ...
systems.
[ See Appendix B.]
See also
* The year
AD 189 or
189 BC
*
List of highways numbered 189
*
References
Integers
{{Num-stub