193 (number)

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← 192 193 194 →
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.

Contents

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]

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

See also

Related Research Articles

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References

  1. ↑ Sloane, N. J. A. (ed.). "SequenceA032020(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.). "SequenceA001913(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.). "SequenceA005109(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.). "SequenceA006512(Greater of twin primes.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-03-02.
  6. ↑ Sloane, N. J. A. (ed.). "SequenceA022005(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.). "SequenceA136162(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. 1 2 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.). "SequenceA007676(Numerators of convergents to e.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-03-02.
  12. ↑ Sloane, N. J. A. (ed.). "SequenceA007677(Denominators of convergents to e.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-03-02.
  13. ↑ Sloane, N. J. A. (ed.). "SequenceA002267(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.
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