149

149 is a natural number that follows 148 and precedes 150. In mathematics, it is a prime number and the 35th prime. It is odd and square-free, with no positive divisors other than 1 and 149. The number is congruent to 1 modulo 4, and it can be written as the sum of two squares: 149 = 10^2 + 7^2.

Representations of 149 in various bases include binary 10010101, octal 225, and hexadecimal 0x95. In base 3 it equals 12112_3. In Roman numerals, 149 is written as CXLIX.

As a calendar year, 149 CE occurred during the Roman Empire in the 2nd century, within the reign of Emperor Antoninus Pius, a period characterized by relative stability and consolidation of the empire. The year is part of the broader historical era known as the Antonine period, which encompassed cultural and administrative developments across the Roman world.

In number theory, 149 is of interest for its primality and its expression as a sum of two squares, illustrating common properties of primes congruent to 1 mod 4. Beyond mathematics, the number 149 appears in various cataloging and designation contexts, but its prominence is primarily mathematical rather than cultural or scientific.