10013 has 8 divisors (see below), whose sum is σ = 11520. Its totient is φ = 8640.

The previous prime is 10009. The next prime is 10037. The reversal of 10013 is 31001.

It is a sphenic number, since it is the product of 3 distinct primes.

It is a cyclic number.

It is not a de Polignac number, because 10013 - 2² = 10009 is a prime.

It is a Duffinian number.

It is a junction number, because it is equal to n+sod(n) for n = 9979 and 10006.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (10093) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 308 + ... + 338.

It is an arithmetic number, because the mean of its divisors is an integer number (1440).

2¹⁰⁰¹³ is an apocalyptic number.

It is an amenable number.

10013 is a deficient number, since it is larger than the sum of its proper divisors (1507).

10013 is a wasteful number, since it uses less digits than its factorization.

10013 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 67.

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

The square root of 10013 is about 100.0649788887. The cubic root of 10013 is about 21.5536787413.

Adding to 10013 its reverse (31001), we get a palindrome (41014).

It can be divided in two parts, 1001 and 3, that multiplied together give a palindrome (3003).

The spelling of 10013 in words is "ten thousand, thirteen".