4131382413312 has 1920 divisors, whose sum is σ = 16781821056000. Its totient is φ = 979880509440.

The previous prime is 4131382413307. The next prime is 4131382413349. The reversal of 4131382413312 is 2133142831314.

4131382413312 is a `hidden beast` number, since 4 + 1 + 313 + 8 + 2 + 4 + 1 + 331 + 2 = 666.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a nude number because it is divisible by every one of its digits and also a Zuckerman number because it is divisible by the product of its digits.

It is an unprimeable number.

It is a polite number, since it can be written in 159 ways as a sum of consecutive naturals, for example, 7038129883 + ... + 7038130469.

It is an arithmetic number, because the mean of its divisors is an integer number (8740531800).

Almost surely, 2^{4131382413312} is an apocalyptic number.

4131382413312 is a gapful number since it is divisible by the number (42) 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 4131382413312, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (8390910528000).

4131382413312 is an abundant number, since it is smaller than the sum of its proper divisors (12650438642688).

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

4131382413312 is a wasteful number, since it uses less digits than its factorization.

4131382413312 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 687 (or 658 counting only the distinct ones).

The product of its digits is 41472, while the sum is 36.

The spelling of 4131382413312 in words is "four trillion, one hundred thirty-one billion, three hundred eighty-two million, four hundred thirteen thousand, three hundred twelve".