1001003112000 has 672 divisors, whose sum is σ = 3816269065440. Its totient is φ = 249584025600.

The previous prime is 1001003111989. The next prime is 1001003112077. The reversal of 1001003112000 is 2113001001.

It can be written as a sum of positive squares in 16 ways, for example, as 351070470144 + 649932641856 = 592512^2 + 806184^2 .

It is a Harshad number since it is a multiple of its sum of digits (9).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 192165396 + ... + 192170604.

Almost surely, 2^{1001003112000} is an apocalyptic number.

1001003112000 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 1001003112000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1908134532720).

1001003112000 is an abundant number, since it is smaller than the sum of its proper divisors (2815265953440).

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

1001003112000 is a wasteful number, since it uses less digits than its factorization.

1001003112000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 5416 (or 5393 counting only the distinct ones).

The product of its (nonzero) digits is 6, while the sum is 9.

Adding to 1001003112000 its reverse (2113001001), we get a palindrome (1003116113001).

The spelling of 1001003112000 in words is "one trillion, one billion, three million, one hundred twelve thousand".