# 193 (number)

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

 ← 192 193 194 →
Cardinalone hundred ninety-three
Ordinal193rd
(one hundred ninety-third)
Factorizationprime
Prime44th
Divisors1, 193
Greek numeralΡϞΓ´
Roman numeralCXCIII
Binary110000012
Ternary210113
Senary5216
Octal3018
Duodecimal14112

## In mathematics

193 is a Pierpont prime number, implying that a 193-gon can be constructed using a compass, straightedge, and angle trisector. It is the number of compositions of 14 into distinct parts.

• It is the only odd prime $p$  known for which 2 is not a primitive root of $4p^{2}+1$ .
• It is part of the fourteenth pair of twin primes $(191,193)$ , the seventh trio of prime triplets $(193,197,199)$ , and the fourth set of prime quadruplets $(191,193,197,199)$ .
• It is the tenth tribonacci number of the form $a(n)=a(n-1)+a(n-2)+a(n-3)$ , with $a(0)=a(1)=a(2)=1$ .
• In decimal, it is the 17th full repetend prime, or long prime.

Aside from itself, the friendly giant, the largest sporadic group, holds a total of 193 conjugacy classes. It also holds at least 44 maximal subgroups (the forty-fourth prime number is 193).

193 is the eighth numerator of convergents to Euler's number; correct to three decimal places: $e\approx {\frac {193}{71}}\approx 2.718\;{\color {red}309\;859\;\ldots }$   The denominator is 71, which is the largest supersingular prime that uniquely divides the order of the friendly giant.