513213204000 has 768 divisors, whose sum is σ = 2073190339584. Its totient is φ = 108306432000.

The previous prime is 513213203963. The next prime is 513213204011. The reversal of 513213204000 is 402312315.

It is a Harshad number since it is a multiple of its sum of digits (21).

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 127 ways as a sum of consecutive naturals, for example, 75680610 + ... + 75687390.

It is an arithmetic number, because the mean of its divisors is an integer number (2699466588).

Almost surely, 2^513213204000 is an apocalyptic number.

513213204000 is a gapful number since it is divisible by the number (50) 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 513213204000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1036595169792).

513213204000 is an abundant number, since it is smaller than the sum of its proper divisors (1559977135584).

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

513213204000 is a wasteful number, since it uses less digits than its factorization.

513213204000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 6886 (or 6868 counting only the distinct ones).

The product of its (nonzero) digits is 720, while the sum is 21.

Adding to 513213204000 its reverse (402312315), we get a palindrome (513615516315).

The spelling of 513213204000 in words is "five hundred thirteen billion, two hundred thirteen million, two hundred four thousand".