513114352128 has 720 divisors, whose sum is σ = 1891929783744. Its totient is φ = 137952460800.

The previous prime is 513114352123. The next prime is 513114352133. The reversal of 513114352128 is 821253411315.

513114352128 is a `hidden beast` number, since 5 + 1 + 3 + 1 + 1 + 435 + 212 + 8 = 666.

It is an interprime number because it is at equal distance from previous prime (513114352123) and next prime (513114352133).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a zygodrome in base 16.

It is a junction number, because it is equal to n+sod(n) for n = 513114352092 and 513114352101.

It is not an unprimeable number, because it can be changed into a prime (513114352123) by changing a digit.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 103636053 + ... + 103641003.

Almost surely, 2^513114352128 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 513114352128, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (945964891872).

513114352128 is an abundant number, since it is smaller than the sum of its proper divisors (1378815431616).

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

513114352128 is an equidigital number, since it uses as much as digits as its factorization.

513114352128 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 5015 (or 4980 counting only the distinct ones).

The product of its digits is 28800, while the sum is 36.

The spelling of 513114352128 in words is "five hundred thirteen billion, one hundred fourteen million, three hundred fifty-two thousand, one hundred twenty-eight".