4005 has 12 divisors (see below), whose sum is σ = 7020. Its totient is φ = 2112.

The previous prime is 4003. The next prime is 4007. The reversal of 4005 is 5004.

4005 is nontrivially palindromic in base 14.

4005 is a nontrivial binomial coefficient, being equal to C(90, 2).

It is an interprime number because it is at equal distance from previous prime (4003) and next prime (4007).

It can be written as a sum of positive squares in 2 ways, for example, as 1089 + 2916 = 33^2 + 54^2 .

It is not a de Polignac number, because 4005 - 2¹ = 4003 is a prime.

It is a Harshad number since it is a multiple of its sum of digits (9).

It is a Curzon number.

It is a plaindrome in base 12.

It is a nialpdrome in base 4, base 9 and base 16.

It is a zygodrome in base 4.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (4001) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 1 + ... + 89.

It is an arithmetic number, because the mean of its divisors is an integer number (585).

4005 is a gapful number since it is divisible by the number (45) formed by its first and last digit.

4005 is the 89-th triangular number and also the 45-th hexagonal number.

It is an amenable number.

4005 is a deficient number, since it is larger than the sum of its proper divisors (3015).

4005 is a wasteful number, since it uses less digits than its factorization.

4005 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 100 (or 97 counting only the distinct ones).

The product of its (nonzero) digits is 20, while the sum is 9.

The square root of 4005 is about 63.2850693292. The cubic root of 4005 is about 15.8806219367.

Adding to 4005 its reverse (5004), we get a palindrome (9009).

Subtracting 4005 from its reverse (5004), we obtain a palindrome (999).

The spelling of 4005 in words is "four thousand, five".