193 (number)
From HandWiki
Short description: Natural number
| ||||
|---|---|---|---|---|
| Cardinal | one hundred ninety-three | |||
| Ordinal | 193rd (one hundred ninety-third) | |||
| Factorization | prime | |||
| Prime | 44th | |||
| Divisors | 1, 193 | |||
| Greek numeral | ΡϞΓ´ | |||
| Roman numeral | CXCIII | |||
| Binary | 110000012 | |||
| Ternary | 210113 | |||
| Quaternary | 30014 | |||
| Quinary | 12335 | |||
| Senary | 5216 | |||
| Octal | 3018 | |||
| Duodecimal | 14112 | |||
| Hexadecimal | C116 | |||
| Vigesimal | 9D20 | |||
| Base 36 | 5D36 | |||
193 (one hundred [and] ninety-three) is the natural number following 192 and preceding 194.
In mathematics
193 is the number of compositions of 14 into distinct parts.[1] In decimal, it is the seventeenth full repetend prime, or long prime.[2]
- It is the only odd prime [math]\displaystyle{ p }[/math] known for which 2 is not a primitive root of [math]\displaystyle{ 4p^2 + 1 }[/math].[3]
- It is the thirteenth Pierpont prime, which implies that a regular 193-gon can be constructed using a compass, straightedge, and angle trisector.[4]
- It is part of the fourteenth pair of twin primes [math]\displaystyle{ (191, 193) }[/math],[5] the seventh trio of prime triplets [math]\displaystyle{ (193, 197, 199) }[/math],[6] and the fourth set of prime quadruplets [math]\displaystyle{ (191, 193, 197, 199) }[/math].[7]
Aside from itself, the friendly giant (the largest sporadic group) holds a total of 193 conjugacy classes.[8] It also holds at least 44 maximal subgroups aside from the double cover of [math]\displaystyle{ \mathbb {B} }[/math] (the forty-fourth prime number is 193).[8][9][10]
193 is also the eighth numerator of convergents to Euler's number; correct to three decimal places: [math]\displaystyle{ e \approx \tfrac{193}{71} \approx 2.718\;{\color{red}309\;859\;\ldots} }[/math] [11] The denominator is 71, which is the largest supersingular prime that uniquely divides the order of the friendly giant.[12][13][14]
In other fields
- 193 is the telephonic number of the 27 Brazilian Military Firefighters Corpses.
- 193 is the number of internationally recognized nations by the United Nations Organization (UNO).
See also
- 193 (disambiguation)
References
- ↑ Sloane, N. J. A., ed. "Sequence A032020 (Number of compositions (ordered partitions) of n into distinct parts)". OEIS Foundation. https://oeis.org/A032020. Retrieved 2022-05-24.
- ↑ Sloane, N. J. A., ed. "Sequence A001913 (Full reptend primes: primes with primitive root 10.)". OEIS Foundation. https://oeis.org/A001913. Retrieved 2023-03-02.
- ↑ E. Friedman, "What's Special About This Number " Accessed 2 January 2006 and again 15 August 2007.
- ↑ Sloane, N. J. A., ed. "Sequence A005109 (Class 1- (or Pierpont) primes: primes of the form 2^t*3^u + 1)". OEIS Foundation. https://oeis.org/A005109.
- ↑ Sloane, N. J. A., ed. "Sequence A006512 (Greater of twin primes.)". OEIS Foundation. https://oeis.org/A006512. Retrieved 2023-03-02.
- ↑ Sloane, N. J. A., ed. "Sequence A022005 (Initial members of prime triples (p, p+4, p+6).)". OEIS Foundation. https://oeis.org/A022005. Retrieved 2023-03-02.
- ↑ Sloane, N. J. A., ed. "Sequence A136162 (List of prime quadruplets {p, p+2, p+6, p+8}.)". OEIS Foundation. https://oeis.org/A136162. Retrieved 2023-03-02.
- ↑ 8.0 8.1 Wilson, R.A.; Parker, R.A.; Nickerson, S.J.; Bray, J.N. (1999). "ATLAS: Monster group M". https://brauer.maths.qmul.ac.uk/Atlas/v3/spor/M/.
- ↑ Wilson, Robert A. (2016). "Is the Suzuki group Sz(8) a subgroup of the Monster?". Bulletin of the London Mathematical Society 48 (2): 356. doi:10.1112/blms/bdw012. https://qmro.qmul.ac.uk/xmlui/bitstream/123456789/12414/1/Wilson%20Is%20Sz%20%288%29%20a%20subgroup%202016%20Accepted.pdf.
- ↑ Dietrich, Heiko; Lee, Melissa; Popiel, Tomasz (May 2023). The maximal subgroups of the Monster. pp. 1-11.
- ↑ Sloane, N. J. A., ed. "Sequence A007676 (Numerators of convergents to e.)". OEIS Foundation. https://oeis.org/A007676. Retrieved 2023-03-02.
- ↑ Sloane, N. J. A., ed. "Sequence A007677 (Denominators of convergents to e.)". OEIS Foundation. https://oeis.org/A007677. Retrieved 2023-03-02.
- ↑ Sloane, N. J. A., ed. "Sequence A002267 (The 15 supersingular primes: primes dividing order of Monster simple group.)". OEIS Foundation. https://oeis.org/A002267. Retrieved 2023-03-02.
- ↑ Luis J. Boya (2011-01-16). "Introduction to Sporadic Groups". Symmetry, Integrability and Geometry: Methods and Applications 7: 13. doi:10.3842/SIGMA.2011.009. Bibcode: 2011SIGMA...7..009B.
 |  |
