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, 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]

See also

• 193 (disambiguation)