13513 has 2 divisors, whose sum is σ = 13514. Its totient is φ = 13512.

The previous prime is 13499. The next prime is 13523. The reversal of 13513 is 31531.

13513 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., 11664 + 1849 = 108^2 + 43^2 .

It is an emirp because it is prime and its reverse (31531) is a distict prime.

It is a cyclic number.

It is not a de Polignac number, because 13513 - 2⁹ = 13001 is a prime.

13513 is a lucky number.

It is a junction number, because it is equal to n+sod(n) for n = 13493 and 13502.

It is a congruent number.

It is not a weakly prime, because it can be changed into another prime (13523) 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, 6756 + 6757.

It is an arithmetic number, because the mean of its divisors is an integer number (6757).

2¹³⁵¹³ is an apocalyptic number.

It is an amenable number.

13513 is a deficient number, since it is larger than the sum of its proper divisors (1).

13513 is an equidigital number, since it uses as much as digits as its factorization.

13513 is an odious number, because the sum of its binary digits is odd.

The product of its digits is 45, while the sum is 13.

The square root of 13513 is about 116.2454300177. The cubic root of 13513 is about 23.8186563696.

The spelling of 13513 in words is "thirteen thousand, five hundred thirteen".