413314100001000 has 192 divisors, whose sum is σ = 1524001809096000. Its totient is φ = 100197357552000.

The previous prime is 413314100000993. The next prime is 413314100001001. The reversal of 413314100001000 is 100001413314.

It is a super-3 number, since 3×413314100001000³ (a number of 45 digits) contains 333 as substring.

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 (413314100001001) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 2087345950 + ... + 2087543949.

It is an arithmetic number, because the mean of its divisors is an integer number (7937509422375).

Almost surely, 2^{413314100001000} is an apocalyptic number.

413314100001000 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

It is an amenable number.

413314100001000 is an abundant number, since it is smaller than the sum of its proper divisors (1110687709095000).

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

413314100001000 is a wasteful number, since it uses less digits than its factorization.

413314100001000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 4174889937 (or 4174889920 counting only the distinct ones).

The product of its (nonzero) digits is 144, while the sum is 18.

Adding to 413314100001000 its reverse (100001413314), we get a palindrome (413414101414314).

It can be divided in two parts, 413 and 314100001000, that added together give a palindrome (314100001413).

The spelling of 413314100001000 in words is "four hundred thirteen trillion, three hundred fourteen billion, one hundred million, one thousand".