101000100100001 has 2 divisors, whose sum is σ = 101000100100002. Its totient is φ = 101000100100000.

The previous prime is 101000100099959. The next prime is 101000100100007. The reversal of 101000100100001 is 100001001000101.

It is a strong prime.

It can be written as a sum of positive squares in only one way, i.e., 100236119216401 + 763980883600 = 10011799^2 + 874060^2 .

It is a cyclic number.

It is not a de Polignac number, because 101000100100001 - 2⁴² = 96602053588897 is a prime.

It is not a weakly prime, because it can be changed into another prime (101000100100007) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (29) of ones.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 50500050050000 + 50500050050001.

It is an arithmetic number, because the mean of its divisors is an integer number (50500050050001).

Almost surely, 2^{101000100100001} is an apocalyptic number.

It is an amenable number.

101000100100001 is a deficient number, since it is larger than the sum of its proper divisors (1).

101000100100001 is an equidigital number, since it uses as much as digits as its factorization.

101000100100001 is an odious number, because the sum of its binary digits is odd.

The product of its (nonzero) digits is 1, while the sum is 5.

Adding to 101000100100001 its reverse (100001001000101), we get a palindrome (201001101100102).

The spelling of 101000100100001 in words is "one hundred one trillion, one hundred million, one hundred thousand, one".