| ||||
|---|---|---|---|---|
| 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 | |||
| Senary | 5216 | |||
| Octal | 3018 | |||
| Duodecimal | 14112 | |||
| Hexadecimal | C116 | |||
193 (one hundred [and] ninety-three) is the natural number following 192 and preceding 194.
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Transcription
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 known for which 2 is not a primitive root of .[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 ,[5] the seventh trio of prime triplets ,[6] and the fourth set of prime quadruplets .[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 (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: [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 Corps.
- 193 is the number of internationally recognized nations by the United Nations Organization (UNO).
See also
References
- ^ Sloane, N. J. A. (ed.). "Sequence A032020 (Number of compositions (ordered partitions) of n into distinct parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-24.
- ^ Sloane, N. J. A. (ed.). "Sequence A001913 (Full reptend primes: primes with primitive root 10.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-03-02.
- ^ E. Friedman, "What's Special About This Number Archived 2018-02-23 at the Wayback Machine" 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)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006512 (Greater of twin primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-03-02.
- ^ Sloane, N. J. A. (ed.). "Sequence A022005 (Initial members of prime triples (p, p+4, p+6).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-03-02.
- ^ Sloane, N. J. A. (ed.). "Sequence A136162 (List of prime quadruplets {p, p+2, p+6, p+8}.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-03-02.
- ^ a b Wilson, R.A.; Parker, R.A.; Nickerson, S.J.; Bray, J.N. (1999). "ATLAS: Monster group M". ATLAS of Finite Group Representations.
- ^ Wilson, Robert A. (2016). "Is the Suzuki group Sz(8) a subgroup of the Monster?" (PDF). Bulletin of the London Mathematical Society. 48 (2): 356. doi:10.1112/blms/bdw012. MR 3483073. S2CID 123219818.
- ^ Dietrich, Heiko; Lee, Melissa; Popiel, Tomasz (May 2023). "The maximal subgroups of the Monster": 1–11. arXiv:2304.14646. S2CID 258676651.
{{cite journal}}: Cite journal requires|journal=(help) - ^ Sloane, N. J. A. (ed.). "Sequence A007676 (Numerators of convergents to e.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-03-02.
- ^ Sloane, N. J. A. (ed.). "Sequence A007677 (Denominators of convergents to e.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-03-02.
- ^ Sloane, N. J. A. (ed.). "Sequence A002267 (The 15 supersingular primes: primes dividing order of Monster simple group.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-03-02.
- ^ Luis J. Boya (2011-01-16). "Introduction to Sporadic Groups". Symmetry, Integrability and Geometry: Methods and Applications. 7: 13. arXiv:1101.3055. Bibcode:2011SIGMA...7..009B. doi:10.3842/SIGMA.2011.009. S2CID 16584404.
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This page was last edited on 18 March 2024, at 14:24