193

193 is a natural number that comes after 192 and before 194. In mathematics it is notable for being a prime number.

As a prime, 193 is the 44th prime. It is congruent to 1 modulo 4 and can be expressed as the sum of two squares: 193 = 12^2 + 7^2. These properties reflect its status as a prime number of the form p ≡ 1 (mod 4).

Representations in different bases include: binary 11000001, octal 301, decimal 193, hexadecimal C1, base 3 21011, and base 5 1233.

In calendars, the 193rd day of a common year is July 12, while in a leap year it falls on July 11.

Historically, the year 193 CE is prominent in Roman history for political upheaval following the death of Commodus. It saw a rapid succession of emperors, including Pertinax and Didius Julianus, and the rise of Septimius Severus along with rival claimants such as Pescennius Niger and Clodius Albinus. The year is often described as a time of upheaval sometimes referred to as the Year of the Five Emperors, reflecting the period’s multiple claimants and rapid changes in leadership.

In Roman numerals, 193 is written as CXCIII.