101000100001000 has 256 divisors, whose sum is σ = 259264128801600. Its totient is φ = 36656750592000.

The previous prime is 101000100000959. The next prime is 101000100001061. The reversal of 101000100001000 is 100001000101.

It can be written as a sum of positive squares in 32 ways, for example, as 7746970422244 + 93253129578756 = 2783338^2 + 9656766^2 .

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

It is an unprimeable number.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 325718032 + ... + 326027968.

Almost surely, 2^{101000100001000} is an apocalyptic number.

101000100001000 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 101000100001000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (129632064400800).

101000100001000 is an abundant number, since it is smaller than the sum of its proper divisors (158264028800600).

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

101000100001000 is a wasteful number, since it uses less digits than its factorization.

101000100001000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 310665 (or 310651 counting only the distinct ones).

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

Adding to 101000100001000 its reverse (100001000101), we get a palindrome (101100101001101).

The spelling of 101000100001000 in words is "one hundred one trillion, one hundred million, one thousand".