From Wikipedia, the free encyclopedia
Natural 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 known for which 2 is not a
primitive root of .
[3]
- It is part of the fourteenth pair of
twin primes ,
[5] the seventh trio of
prime triplets ,
[6] and the fourth set of
prime quadruplets .
[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 (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
References
-
^
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.
-
^
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.
-
^ 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.
-
^
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.
-
^
Sloane, N. J. A. (ed.).
"Sequence A006512 (Greater of twin primes.)". The
On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-03-02.
-
^
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.
-
^
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.
- ^
a
b
Wilson, R.A.;
Parker, R.A.; Nickerson, S.J.; Bray, J.N. (1999).
"ATLAS: Monster group M". ATLAS of Finite Group Representations.
-
^ 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.
-
^ Dietrich, Heiko; Lee, Melissa; Popiel, Tomasz (May 2023). "The maximal subgroups of the Monster": 1–11.
arXiv:
2304.14646.
S2CID
258676651.
-
^
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.
-
^
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.
-
^
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.
-
^ 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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100,000
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1,000,000
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10,000,000
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100,000,000
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1,000,000,000
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