193 (number)

193 (one hundred [and] ninety-three) is the natural number following 192 and preceding 194.

← 192 193 194 →
← 190 191 192 193 194 195 196 197 198 199 → List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
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

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 ${\displaystyle p}$ known for which 2 is not a primitive root of ${\displaystyle 4p^{2}+1}$.^[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 ${\displaystyle (191,193)}$,^[5] the seventh trio of prime triplets ${\displaystyle (193,197,199)}$,^[6] and the fourth set of prime quadruplets ${\displaystyle (191,193,197,199)}$.^[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 ${\displaystyle \mathbb {B} }$ (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: ${\displaystyle e\approx {\tfrac {193}{71}}\approx 2.718\;{\color {red}309\;859\;\ldots }}$ ^[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

• 193 (disambiguation)

References

1. 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.
2. 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.
3. 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.
4. 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.
5. Sloane, N. J. A. (ed.). "Sequence A006512 (Greater of twin primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-03-02.
6. 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.
7. 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.
8. Wilson, R.A.; Parker, R.A.; Nickerson, S.J.; Bray, J.N. (1999). "ATLAS: Monster group M". ATLAS of Finite Group Representations.
9. 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.
10. 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)
11. 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.
12. 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.
13. 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.
14. 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.