4001 has 2 divisors, whose sum is σ = 4002. Its totient is φ = 4000.

The previous prime is 3989. The next prime is 4003. The reversal of 4001 is 1004.

It is a strong prime.

It can be written as a sum of positive squares in only one way, i.e., 2401 + 1600 = 49^2 + 40^2 .

It is a cyclic number.

It is a de Polignac number, because none of the positive numbers 2^k-4001 is a prime.

Together with 4003, it forms a pair of twin primes.

It is a Chen prime.

It is a magnanimous number.

It is a plaindrome in base 7 and base 15.

It is a nialpdrome in base 8 and base 16.

It is not a weakly prime, because it can be changed into another prime (4003) by changing a digit.

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

It is a good prime.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 2000 + 2001.

It is an arithmetic number, because the mean of its divisors is an integer number (2001).

It is an amenable number.

4001 is a deficient number, since it is larger than the sum of its proper divisors (1).

4001 is an equidigital number, since it uses as much as digits as its factorization.

4001 is an odious number, because the sum of its binary digits is odd.

The product of its (nonzero) digits is 4, while the sum is 5.

The square root of 4001 is about 63.2534584035. The cubic root of 4001 is about 15.8753332437.

Adding to 4001 its reverse (1004), we get a palindrome (5005).

The spelling of 4001 in words is "four thousand, one", and thus it is an iban number.