10100010000100 has 144 divisors (see below), whose sum is σ = 24042870064080. Its totient is φ = 3665675059200.

The previous prime is 10100010000097. The next prime is 10100010000137. The reversal of 10100010000100 is 100001000101.

10100010000100 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in 24 ways, for example, as 3242441259684 + 6857568740416 = 1800678^2 + 2618696^2 .

It is a Harshad number since it is a multiple of its sum of digits (4).

It is a self number, because there is not a number n which added to its sum of digits gives 10100010000100.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 32432332 + ... + 32742268.

It is an arithmetic number, because the mean of its divisors is an integer number (166964375445).

Almost surely, 2^{10100010000100} is an apocalyptic number.

10100010000100 is a gapful number since it is divisible by the number (10) 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 10100010000100, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (12021435032040).

10100010000100 is an abundant number, since it is smaller than the sum of its proper divisors (13942860063980).

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

10100010000100 is a wasteful number, since it uses less digits than its factorization.

10100010000100 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 310658 (or 310651 counting only the distinct ones).

The product of its (nonzero) digits is 1, while the sum is 4.

Adding to 10100010000100 its reverse (100001000101), we get a palindrome (10200011000201).

The spelling of 10100010000100 in words is "ten trillion, one hundred billion, ten million, one hundred", and thus it is an aban number.