193 (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. In decimal, it is the seventeenth full repetend prime, or long prime.

• It is the only odd prime $p$ known for which 2 is not a primitive root of $4p^2+1$.

• It is the thirteenth Pierpont prime, which implies that a regular 193-gon can be constructed using a compass, straightedge, and angle trisector.

• 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 $(191,193,197,199)$.

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 aside from the double cover of $\mathbb{𝔹}$ (the forty-fourth prime number is 193).

193 is also the eighth numerator of convergents to Euler's number; correct to three decimal places: $e\approx \frac{193}{71}\approx 2.718309859\dots$ The denominator is 71, which is the largest supersingular prime that uniquely divides the order of the friendly giant.

See also

• 193 (disambiguation)