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189 (number)

← 188 189 190 →
Cardinalone hundred eighty-nine
Ordinal189th
(one hundred eighty-ninth)
Factorization33 × 7
Greek numeralΡΠΘ´
Roman numeralCLXXXIX
Binary101111012
Ternary210003
Senary5136
Octal2758
Duodecimal13912
HexadecimalBD16

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]

There are 189 zeros among the decimal digits of the positive integers with at most three digits.[5]

The largest prime number that can be represented in 256-bit arithmetic is the "ultra-useful prime" 2256 − 189,[6] used in quasi-Monte Carlo methods[7] and in some cryptographic systems.[8]

See also

References

Wikimedia Commons has media related to 189 (number).
  1. ^ Sloane, N. J. A. (ed.). "Sequence A005898 (Centered cube numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^ Sloane, N. J. A. (ed.). "Sequence A000566 (Heptagonal numbers)". The On-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)". The On-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)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ^ Sloane, N. J. A. (ed.). "Sequence A033713 (Number of zeros in numbers 1 to 999..9 (n digits))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  6. ^ Sloane, N. J. A. (ed.). "Sequence A058220 (Ultra-useful primes: smallest k such that 2^(2^n) - k is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  7. ^ 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.
  8. ^ 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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