101313000313101 has 12 divisors (see below), whose sum is σ = 147789921250140. Its totient is φ = 66873267532800.

The previous prime is 101313000313081. The next prime is 101313000313111.

101313000313101 is a `hidden beast` number, since 10 + 1 + 31 + 300 + 0 + 313 + 10 + 1 = 666.

101313000313101 is nontrivially palindromic in base 10.

It can be written as a sum of positive squares in 2 ways, for example, as 98960197119876 + 2352803193225 = 9947874^2 + 1533885^2 .

It is not a de Polignac number, because 101313000313101 - 2⁵ = 101313000313069 is a prime.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (101313000313111) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 55727722036 + ... + 55727723853.

It is an arithmetic number, because the mean of its divisors is an integer number (12315826770845).

Almost surely, 2^{101313000313101} is an apocalyptic number.

It is an amenable number.

101313000313101 is a deficient number, since it is larger than the sum of its proper divisors (46476920937039).

101313000313101 is a wasteful number, since it uses less digits than its factorization.

101313000313101 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 111455445996 (or 111455445993 counting only the distinct ones).

The product of its (nonzero) digits is 81, while the sum is 18.

It can be divided in two parts, 101313000 and 313101, that added together give a palindrome (101626101).

The spelling of 101313000313101 in words is "one hundred one trillion, three hundred thirteen billion, three hundred thirteen thousand, one hundred one".