Английская Википедия:193 (number)
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>p</math> known for which 2 is not a primitive root of <math>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>(191, 193)</math>,[5] the seventh trio of prime triplets <math>(193, 197, 199)</math>,[6] and the fourth set of prime quadruplets <math>(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>\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>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
References
Шаблон:Commons category Шаблон:Integers
- ↑ Шаблон:Cite OEIS
- ↑ Шаблон:Cite OEIS
- ↑ E. Friedman, "What's Special About This Number Шаблон:Webarchive" Accessed 2 January 2006 and again 15 August 2007.
- ↑ Шаблон:Cite OEIS
- ↑ Шаблон:Cite OEIS
- ↑ Шаблон:Cite OEIS
- ↑ Шаблон:Cite OEIS
- ↑ 8,0 8,1 Шаблон:Cite web
- ↑ Шаблон:Cite journal
- ↑ Шаблон:Cite journal
- ↑ Шаблон:Cite OEIS
- ↑ Шаблон:Cite OEIS
- ↑ Шаблон:Cite OEIS
- ↑ Шаблон:Cite journal
