13009 has 2 divisors, whose sum is σ = 13010. Its totient is φ = 13008.

The previous prime is 13007. The next prime is 13033. The reversal of 13009 is 90031.

It is a happy number.

13009 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a weak prime.

It can be written as a sum of positive squares in only one way, i.e., 9409 + 3600 = 97^2 + 60^2 .

It is an emirp because it is prime and its reverse (90031) is a distict prime.

It is a cyclic number.

It is not a de Polignac number, because 13009 - 2¹ = 13007 is a prime.

Together with 13007, it forms a pair of twin primes.

It is a Chen prime.

13009 is a lucky number.

It is a nialpdrome in base 12.

It is a self number, because there is not a number n which added to its sum of digits gives 13009.

It is not a weakly prime, because it can be changed into another prime (13001) 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, 6504 + 6505.

It is an arithmetic number, because the mean of its divisors is an integer number (6505).

2¹³⁰⁰⁹ is an apocalyptic number.

It is an amenable number.

13009 is a deficient number, since it is larger than the sum of its proper divisors (1).

13009 is an equidigital number, since it uses as much as digits as its factorization.

13009 is an odious number, because the sum of its binary digits is odd.

The product of its (nonzero) digits is 27, while the sum is 13.

The square root of 13009 is about 114.0570032922. The cubic root of 13009 is about 23.5187717825.

Subtracting from 13009 its sum of digits (13), we obtain a square (12996 = 114²).

The spelling of 13009 in words is "thirteen thousand, nine".