100001121100001 has 12 divisors (see below), whose sum is σ = 111006890517012. Its totient is φ = 90010009980000.

The previous prime is 100001121099991. The next prime is 100001121100163.

It is a happy number.

100001121100001 is nontrivially palindromic in base 10.

It can be written as a sum of positive squares in 2 ways, for example, as 94589337747025 + 5411783352976 = 9725705^2 + 2326324^2 .

It is not a de Polignac number, because 100001121100001 - 2³⁰ = 100000047358177 is a prime.

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (100001121160001) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 4091351870 + ... + 4091376311.

It is an arithmetic number, because the mean of its divisors is an integer number (9250574209751).

Almost surely, 2^{100001121100001} is an apocalyptic number.

100001121100001 is a gapful number since it is divisible by the number (11) formed by its first and last digit.

It is an amenable number.

100001121100001 is a deficient number, since it is larger than the sum of its proper divisors (11005769417011).

100001121100001 is a wasteful number, since it uses less digits than its factorization.

100001121100001 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 8182728304 (or 8182728293 counting only the distinct ones).

The product of its (nonzero) digits is 2, while the sum is 8.

The spelling of 100001121100001 in words is "one hundred trillion, one billion, one hundred twenty-one million, one hundred thousand, one".