102112122001000 has 128 divisors (see below), whose sum is σ = 244809693666720. Its totient is φ = 39842208000000.

The previous prime is 102112122000983. The next prime is 102112122001007. The reversal of 102112122001000 is 100221211201.

It can be written as a sum of positive squares in 16 ways, for example, as 4822266673156 + 97289855327844 = 2195966^2 + 9863562^2 .

It is not an unprimeable number, because it can be changed into a prime (102112122001007) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 258143370 + ... + 258538630.

Almost surely, 2^{102112122001000} is an apocalyptic number.

102112122001000 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 102112122001000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (122404846833360).

102112122001000 is an abundant number, since it is smaller than the sum of its proper divisors (142697571665720).

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

102112122001000 is a wasteful number, since it uses less digits than its factorization.

102112122001000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 401624 (or 401610 counting only the distinct ones).

The product of its (nonzero) digits is 16, while the sum is 13.

Adding to 102112122001000 its reverse (100221211201), we get a palindrome (102212343212201).

The spelling of 102112122001000 in words is "one hundred two trillion, one hundred twelve billion, one hundred twenty-two million, one thousand".