101312312112000 has 1024 divisors, whose sum is σ = 409161524428800. Its totient is φ = 24435661824000.

The previous prime is 101312312111987. The next prime is 101312312112019. The reversal of 101312312112000 is 211213213101.

101312312112000 is a `hidden beast` number, since 10 + 1 + 312 + 312 + 11 + 20 + 0 + 0 = 666.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (23) of ones.

It is a polite number, since it can be written in 127 ways as a sum of consecutive naturals, for example, 936089889 + ... + 936198111.

It is an arithmetic number, because the mean of its divisors is an integer number (399571801200).

Almost surely, 2^{101312312112000} is an apocalyptic number.

101312312112000 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 101312312112000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (204580762214400).

101312312112000 is an abundant number, since it is smaller than the sum of its proper divisors (307849212316800).

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

101312312112000 is a wasteful number, since it uses less digits than its factorization.

101312312112000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 108469 (or 108441 counting only the distinct ones).

The product of its (nonzero) digits is 72, while the sum is 18.

Adding to 101312312112000 its reverse (211213213101), we get a palindrome (101523525325101).

The spelling of 101312312112000 in words is "one hundred one trillion, three hundred twelve billion, three hundred twelve million, one hundred twelve thousand".