# 193 (number)

Short description: Natural number
 ← 192 193 194 →
Cardinalone hundred ninety-three
Ordinal193rd
(one hundred ninety-third)
Factorizationprime
Prime44th
Divisors1, 193
Greek numeralΡϞΓ´
Roman numeralCXCIII
Binary110000012
Ternary210113
Quaternary30014
Quinary12335
Senary5216
Octal3018
Duodecimal14112
Vigesimal9D20
Base 365D36

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 $\displaystyle{ p }$ known for which 2 is not a primitive root of $\displaystyle{ 4p^2 + 1 }$.[3]
• 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 Corpses.
• 193 is the number of internationally recognized nations by the United Nations Organization (UNO).

• 193 (disambiguation)

## References

1. Sloane, N. J. A., ed. "Sequence A032020 (Number of compositions (ordered partitions) of n into distinct parts)". OEIS Foundation. Retrieved 2022-05-24.
2. Sloane, N. J. A., ed. "Sequence A001913 (Full reptend primes: primes with primitive root 10.)". OEIS Foundation. Retrieved 2023-03-02.
3. E. Friedman, "What's Special About This Number " Accessed 2 January 2006 and again 15 August 2007.
4. Sloane, N. J. A., ed. "Sequence A006512 (Greater of twin primes.)". OEIS Foundation. Retrieved 2023-03-02.
5. Sloane, N. J. A., ed. "Sequence A022005 (Initial members of prime triples (p, p+4, p+6).)". OEIS Foundation. Retrieved 2023-03-02.
6. Sloane, N. J. A., ed. "Sequence A136162 (List of prime quadruplets {p, p+2, p+6, p+8}.)". OEIS Foundation. Retrieved 2023-03-02.
7. Wilson, R.A.; Parker, R.A.; Nickerson, S.J.; Bray, J.N. (1999). "ATLAS: Monster group M".
8. 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.
9. Dietrich, Heiko; Lee, Melissa; Popiel, Tomasz (May 2023). The maximal subgroups of the Monster. pp. 1-11.
10. Sloane, N. J. A., ed. "Sequence A007676 (Numerators of convergents to e.)". OEIS Foundation. Retrieved 2023-03-02.
11. Sloane, N. J. A., ed. "Sequence A007677 (Denominators of convergents to e.)". OEIS Foundation. Retrieved 2023-03-02.
12. Sloane, N. J. A., ed. "Sequence A002267 (The 15 supersingular primes: primes dividing order of Monster simple group.)". OEIS Foundation. Retrieved 2023-03-02.
13. 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. Bibcode2011SIGMA...7..009B.