2013013002000 has 960 divisors, whose sum is σ = 8869572811008. Its totient is φ = 386104320000.

The previous prime is 2013013001957. The next prime is 2013013002043. The reversal of 2013013002000 is 2003103102.

It is a happy number.

2013013002000 is digitally balanced in base 12, because in such base it contains all the possibile digits an equal number of times.

It is an interprime number because it is at equal distance from previous prime (2013013001957) and next prime (2013013002043).

It is a Harshad number since it is a multiple of its sum of digits (12).

2013013002000 is strictly pandigital in base 12.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 42018060 + ... + 42065940.

Almost surely, 2^{2013013002000} is an apocalyptic number.

2013013002000 is a gapful number since it is divisible by the number (20) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 2013013002000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (4434786405504).

2013013002000 is an abundant number, since it is smaller than the sum of its proper divisors (6856559809008).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

2013013002000 is a wasteful number, since it uses less digits than its factorization.

2013013002000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 47945 (or 47922 counting only the distinct ones).

The product of its (nonzero) digits is 36, while the sum is 12.

Adding to 2013013002000 its reverse (2003103102), we get a palindrome (2015016105102).

The spelling of 2013013002000 in words is "two trillion, thirteen billion, thirteen million, two thousand".