4091 has 2 divisors, whose sum is σ = 4092. Its totient is φ = 4090.

The previous prime is 4079. The next prime is 4093. The reversal of 4091 is 1904.

Added to its reverse (1904) it gives a triangular number (5995 = T₁₀₉).

It is a strong prime.

It is a cyclic number.

It is not a de Polignac number, because 4091 - 2⁶ = 4027 is a prime.

Together with 4093, it forms a pair of twin primes.

It is a Chen prime.

It is equal to p₅₆₃ and since 4091 and 563 have the same sum of digits, it is a Honaker prime.

It is a plaindrome in base 12.

It is a nialpdrome in base 8 and base 16.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 4091.

It is not a weakly prime, because it can be changed into another prime (4093) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 2045 + 2046.

It is an arithmetic number, because the mean of its divisors is an integer number (2046).

2⁴⁰⁹¹ is an apocalyptic number.

4091 is a deficient number, since it is larger than the sum of its proper divisors (1).

4091 is an equidigital number, since it uses as much as digits as its factorization.

4091 is an odious number, because the sum of its binary digits is odd.

The product of its (nonzero) digits is 36, while the sum is 14.

The square root of 4091 is about 63.9609255718. The cubic root of 4091 is about 15.9934869324.

Adding to 4091 its reverse (1904), we get a palindrome (5995).

Subtracting from 4091 its reverse (1904), we obtain a 7-th power (2187 = 3⁷).

It can be divided in two parts, 40 and 91, that added together give a palindrome (131).

The spelling of 4091 in words is "four thousand, ninety-one".