181

181 is the natural number that follows 180 and precedes 182. In mathematics, it is a prime number and, because its decimal representation is the same forwards and backwards, a palindromic prime. It is odd and congruent to 1 modulo 4. In the sequence of primes, 181 is the 42nd prime.

In various representations, 181 appears as follows: in Roman numerals it is CLXXXI, in binary it is 10110101, and in hexadecimal it is 0xB5. It can be expressed as the sum of the squares of consecutive integers: 9^2 + 10^2 = 181, which also satisfies the form 2n^2 + 2n + 1 with n = 9.

Beyond pure mathematics, 181 has uses as an ordinal label in other contexts. It is the designation of the asteroid 181 Eucharis, a large object in the main asteroid belt discovered in 1878. As a calendar year, 181 can refer to 181 BCE or 181 CE, depending on the era referenced.

Summary: 181 is a prime, palindromic number with several simple representations in common bases, and it holds a place in astronomy as the name of a main-belt asteroid. Its mathematical properties include being the sum of consecutive squares and counting as the 42nd prime in the ordinary integer sequence.