1891 has 4 divisors (see below), whose sum is σ = 1984. Its totient is φ = 1800.

The previous prime is 1889. The next prime is 1901. The reversal of 1891 is 1981.

1891 = T₃₄ + T₃₅ + T₃₆.

1891 is a nontrivial binomial coefficient, being equal to C(62, 2).

It is a semiprime because it is the product of two primes, and also a brilliant number, because the two primes have the same length, and also an emirpimes, since its reverse is a distinct semiprime: 1981 = 7 ⋅283.

It is a 3-Lehmer number, since φ(1891) divides (1891-1)³.

It is a cyclic number.

It is not a de Polignac number, because 1891 - 2¹ = 1889 is a prime.

It is a plaindrome in base 11 and base 12.

It is a nialpdrome in base 14, base 15 and base 16.

It is not an unprimeable number, because it can be changed into a prime (1801) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 1 + ... + 61.

It is an arithmetic number, because the mean of its divisors is an integer number (496).

2¹⁸⁹¹ is an apocalyptic number.

1891 is the 61-st triangular number and also the 31-st hexagonal number.

1891 is the 36-th centered triangular number, the 28-th centered pentagonal number and also the 21-st centered nonagonal number.

1891 is a deficient number, since it is larger than the sum of its proper divisors (93).

1891 is an equidigital number, since it uses as much as digits as its factorization.

1891 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 92.

The product of its digits is 72, while the sum is 19.

The square root of 1891 is about 43.4856298103. The cubic root of 1891 is about 12.3660360892.

It can be divided in two parts, 189 and 1, that added together give a triangular number (190 = T₁₉).

The spelling of 1891 in words is "one thousand, eight hundred ninety-one".