13001 has 2 divisors, whose sum is σ = 13002. Its totient is φ = 13000.

The previous prime is 12983. The next prime is 13003. The reversal of 13001 is 10031.

13001 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a strong prime.

It can be written as a sum of positive squares in only one way, i.e., 7225 + 5776 = 85^2 + 76^2 .

It is a cyclic number.

It is a de Polignac number, because none of the positive numbers 2^k-13001 is a prime.

It is a Sophie Germain prime.

Together with 13003, it forms a pair of twin primes.

It is a Chen prime.

It is a Curzon number.

It is not a weakly prime, because it can be changed into another prime (13003) 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 as a sum of consecutive naturals, namely, 6500 + 6501.

It is an arithmetic number, because the mean of its divisors is an integer number (6501).

2¹³⁰⁰¹ is an apocalyptic number.

It is an amenable number.

13001 is a deficient number, since it is larger than the sum of its proper divisors (1).

13001 is an equidigital number, since it uses as much as digits as its factorization.

13001 is an odious number, because the sum of its binary digits is odd.

The product of its (nonzero) digits is 3, while the sum is 5.

The square root of 13001 is about 114.0219277157. The cubic root of 13001 is about 23.5139497681.

Adding to 13001 its reverse (10031), we get a palindrome (23032).

The spelling of 13001 in words is "thirteen thousand, one".