| Number | 189 |
|---|---|
| Divisor | 1, 3, 7, 9, 21, 27, 63, 189 |
189 (one hundred [and] eighty-nine) is the natural number following 188 and preceding 190.
In mathematics
189 is a centered cube number[1] and a heptagonal number.[2] The centered cube numbers are the sums of two consecutive cubes, and 189 can be written as sum of two cubes in two ways: 43 + 53 and 63 + (−3)3.[3] The smallest number that can be written as the sum of two positive cubes in two ways is 1729.[4]
The largest prime number that can be represented in 256-bit arithmetic is the "ultra-useful prime" 2256 − 189,[5] used in quasi-Monte Carlo methods[6] and in some cryptographic systems.[7]
See also
- The year AD 189 or 189 BC
- List of highways numbered 189
References
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- ^ Hechenleitner, Bernhard & Entacher, Karl (2006). "A parallel search for good lattice points using LLL-spectral tests". Journal of Computational and Applied Mathematics. 189 (1–2): 424–441. doi:10.1016/j.cam.2005.03.058. MR 2202988. See Table 5.
- ^ Longa, Patrick & Gebotys, Catherine H. (2010). "Efficient Techniques for High-Speed Elliptic Curve Cryptography". Cryptographic Hardware and Embedded Systems, CHES 2010, 12th International Workshop, Santa Barbara, CA, USA, August 17-20, 2010. Proceedings. Vol. 6225. Lecture Notes in Computer Science. Springer. pp. 80–94. doi:10.1007/978-3-642-15031-9_6. ISBN 978-3-642-15030-2. See Appendix B.