193 (number)

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

In mathematics

193 is the number of

• 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

of ${\displaystyle \mathbb {B} }$ (the forty-fourth prime number is 193).[8]^[9][10]

193 is also the eighth

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. ^ ^{a b} Wilson, R.A.; Parker, R.A.; Nickerson, S.J.; Bray, J.N. (1999). "ATLAS: Monster group M". ATLAS of Finite Group Representations.
9. S2CID 123219818
   .
10. 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. S2CID 16584404
    .

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