189 (number)
| ||||
|---|---|---|---|---|
| Cardinal | one hundred eighty-nine | |||
| Ordinal | 189th (one hundred eighty-ninth) | |||
| Factorization | 33 × 7 | |||
| Greek numeral | ΡΠΘ´ | |||
| Roman numeral | 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.
In mathematics
[edit]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
[edit]References
[edit]
Wikimedia Commons has media related to 189 (number).
- ^ Sloane, N. J. A. (ed.). "Sequence A005898 (Centered cube numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000566 (Heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ 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.
- ^ 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.
- ^ 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.
- ^ 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.
- ^ 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". 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.