1003643312400 has 405 divisors, whose sum is σ = 3555517706949. Its totient is φ = 262172286720.

The previous prime is 1003643312333. The next prime is 1003643312401. The reversal of 1003643312400 is 42133463001.

1003643312400 = 1³ + 2³ + ... + 1415³.

The square root of 1003643312400 is 1001820.

It is a perfect power (a square), and thus also a powerful number.

1003643312400 is a `hidden beast` number, since 1 + 0 + 0 + 3 + 643 + 3 + 12 + 4 + 0 + 0 = 666.

1003643312400 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in only one way, i.e., 361311592464 + 642331719936 = 601092^2 + 801456^2 .

It is not an unprimeable number, because it can be changed into a prime (1003643312401) by changing a digit.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 3546442659 + ... + 3546442941.

Almost surely, 2^{1003643312400} is an apocalyptic number.

1003643312400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

1003643312400 is the 1001820-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 1003643312400

1003643312400 is an abundant number, since it is smaller than the sum of its proper divisors (2551874394549).

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

1003643312400 is an equidigital number, since it uses as much as digits as its factorization.

1003643312400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 708 (or 352 counting only the distinct ones).

The product of its (nonzero) digits is 5184, while the sum is 27.

Adding to 1003643312400 its reverse (42133463001), we get a palindrome (1045776775401).

The spelling of 1003643312400 in words is "one trillion, three billion, six hundred forty-three million, three hundred twelve thousand, four hundred".