189 (number)
| ||||
|---|---|---|---|---|
| Cardinal | one hundred eighty-nine | |||
| Ordinal | 189th (one hundred eighty-ninth) | |||
| Factorization | 33 × 7 | |||
| 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.
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]
189 is the sum of the sums of the divisors of the first 15 positive integers.
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
- ^ 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.