189 (number)

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← 188 189 190 →
Cardinal one hundred eighty-nine
Ordinal 189th
(one hundred eighty-ninth)
Factorization 33 × 7
Divisors 1, 3, 7, 9, 21, 27, 63, 189
Greek numeral ΡΠΘ´
Roman numeral CLXXXIX, clxxxix
Binary 101111012
Ternary 210003
Senary 5136
Octal 2758
Duodecimal 13912
Hexadecimal BD16

189 (one hundred [and] eighty-nine) is the natural number following 188 and preceding 190.

Contents

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

References

  1. ↑ Sloane, N. J. A. (ed.). "SequenceA005898(Centered cube numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  2. ↑ Sloane, N. J. A. (ed.). "SequenceA000566(Heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  3. ↑ Sloane, N. J. A. (ed.). "SequenceA051347(Numbers that are the sum of two (possibly negative) cubes in at least 2 ways)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  4. ↑ Sloane, N. J. A. (ed.). "SequenceA001235(Taxi-cab numbers: sums of 2 cubes in more than 1 way)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  5. ↑ Sloane, N. J. A. (ed.). "SequenceA058220(Ultra-useful primes: smallest k such that 2^(2^n) - k is prime)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  6. ↑ 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.
  7. ↑ Longa, Patrick; Gebotys, Catherine H. (2010). "Efficient Techniques for High-Speed Elliptic Curve Cryptography". In Mangard, Stefan; Standaert, François-Xavier (eds.). Cryptographic Hardware and Embedded Systems, CHES 2010, 12th International Workshop, Santa Barbara, CA, USA, August 17-20, 2010. Proceedings. Lecture Notes in Computer Science. Vol. 6225. Springer. pp. 80–94. doi: 10.1007/978-3-642-15031-9_6 . ISBN   978-3-642-15030-2. See Appendix B.


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