10102101002000 has 320 divisors, whose sum is σ = 28303552742400. Its totient is φ = 3415818240000.

The previous prime is 10102101001997. The next prime is 10102101002003. The reversal of 10102101002000 is 20010120101.

It is an interprime number because it is at equal distance from previous prime (10102101001997) and next prime (10102101002003).

It is a Harshad number since it is a multiple of its sum of digits (8).

It is not an unprimeable number, because it can be changed into a prime (10102101002003) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 363384101 + ... + 363411899.

It is an arithmetic number, because the mean of its divisors is an integer number (88448602320).

Almost surely, 2^{10102101002000} is an apocalyptic number.

10102101002000 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 10102101002000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (14151776371200).

10102101002000 is an abundant number, since it is smaller than the sum of its proper divisors (18201451740400).

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

10102101002000 is a wasteful number, since it uses less digits than its factorization.

10102101002000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 28187 (or 28171 counting only the distinct ones).

The product of its (nonzero) digits is 4, while the sum is 8.

Adding to 10102101002000 its reverse (20010120101), we get a palindrome (10122111122101).

The spelling of 10102101002000 in words is "ten trillion, one hundred two billion, one hundred one million, two thousand".