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189 (number)

From Wikipedia, the free encyclopedia
Natural number
← 188189 190 →
Cardinalone hundred eighty-nine
Ordinal189th
(one hundred eighty-ninth)
Factorization33 × 7
Divisors1, 3, 7, 9, 21, 27, 63, 189
Greek numeralΡΠΘ´
Roman numeralCLXXXIX,clxxxix
Binary101111012
Ternary210003
Senary5136
Octal2758
Duodecimal13912
HexadecimalBD16

189 (one hundred [and] eighty-nine) is thenatural number following188 and preceding190.

In mathematics

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189 is acentered cube number[1] and aheptagonal number.[2]The centered cube numbers are the sums of two consecutivecubes, and 189 can be written assum of two cubes in two ways:43 + 53 and63 + (−3)3.[3] The smallest number that can be written as the sum of two positive cubes in two ways is1729.[4]

The largestprime number that can be represented in 256-bit arithmetic is the "ultra-useful prime"2256 − 189,[5] used inquasi-Monte Carlo methods[6] and in somecryptographic systems.[7]

See also

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References

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Wikimedia Commons has media related to189 (number).
  1. ^Sloane, N. J. A. (ed.)."Sequence A005898 (Centered cube numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^Sloane, N. J. A. (ed.)."Sequence A000566 (Heptagonal numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^Sloane, N. J. A. (ed.)."Sequence A051347 (Numbers that are the sum of two (possibly negative) cubes in at least 2 ways)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^Sloane, N. J. A. (ed.)."Sequence A001235 (Taxi-cab numbers: sums of 2 cubes in more than 1 way)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ^Sloane, N. J. A. (ed.)."Sequence A058220 (Ultra-useful primes: smallest k such that 2^(2^n) - k is prime)".TheOn-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.
0 to 199
200 to 399
400 to 999
1000s and 10,000s
1000s
10,000s
100,000s to 10,000,000,000,000s


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