4000 has 24 divisors (see below), whose sum is σ = 9828. Its totient is φ = 1600.

The previous prime is 3989. The next prime is 4001. The reversal of 4000 is 4.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

4000 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

4000 is an esthetic number in base 9, because in such base its adjacent digits differ by 1.

It can be written as a sum of positive squares in 2 ways, for example, as 2704 + 1296 = 52^2 + 36^2 .

It is a Harshad number since it is a multiple of its sum of digits (4).

It is a super Niven number, because it is divisible the sum of any subset of its (nonzero) digits.

It is a nialpdrome in base 4, base 8, base 10 and base 16.

It is a zygodrome in base 4.

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 3 ways as a sum of consecutive naturals, for example, 798 + ... + 802.

2^{4000} is an apocalyptic number.

4000 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

4000 is the 32-nd decagonal number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 4000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (4914).

4000 is an abundant number, since it is smaller than the sum of its proper divisors (5828).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

4000 is an equidigital number, since it uses as much as digits as its factorization.

4000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 25 (or 7 counting only the distinct ones).

The product of its (nonzero) digits is 4, while the sum is 4.

The square root of 4000 is about 63.2455532034. The cubic root of 4000 is about 15.8740105197.

The spelling of 4000 in words is "four thousand", and thus it is an eban number and an iban number.

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