312121310013000 has 1024 divisors, whose sum is σ = 1126001036160000. Its totient is φ = 79934567731200.

The previous prime is 312121310012999. The next prime is 312121310013001. The reversal of 312121310013000 is 310013121213.

312121310013000 is a `hidden beast` number, since 31 + 2 + 1 + 21 + 310 + 0 + 1 + 300 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (312121310012999) and next prime (312121310013001).

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

It is not an unprimeable number, because it can be changed into a prime (312121310013001) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (29) of ones.

It is a polite number, since it can be written in 255 ways as a sum of consecutive naturals, for example, 12946244946 + ... + 12946269054.

It is an arithmetic number, because the mean of its divisors is an integer number (1099610386875).

Almost surely, 2^{312121310013000} is an apocalyptic number.

312121310013000 is a gapful number since it is divisible by the number (30) 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 312121310013000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (563000518080000).

312121310013000 is an abundant number, since it is smaller than the sum of its proper divisors (813879726147000).

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

312121310013000 is a wasteful number, since it uses less digits than its factorization.

312121310013000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 24384 (or 24364 counting only the distinct ones).

The product of its (nonzero) digits is 108, while the sum is 18.

Adding to 312121310013000 its reverse (310013121213), we get a palindrome (312431323134213).

The spelling of 312121310013000 in words is "three hundred twelve trillion, one hundred twenty-one billion, three hundred ten million, thirteen thousand".