1000101000001 has 2 divisors, whose sum is σ = 1000101000002. Its totient is φ = 1000101000000.

The previous prime is 1000100999923. The next prime is 1000101000023. The reversal of 1000101000001 is 1000001010001.

It is a strong prime.

It can be written as a sum of positive squares in only one way, i.e., 643005119376 + 357095880625 = 801876^2 + 597575^2 .

It is a cyclic number.

It is not a de Polignac number, because 1000101000001 - 2¹³ = 1000100991809 is a prime.

It is not a weakly prime, because it can be changed into another prime (1000101000061) 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 as a sum of consecutive naturals, namely, 500050500000 + 500050500001.

It is an arithmetic number, because the mean of its divisors is an integer number (500050500001).

Almost surely, 2^{1000101000001} is an apocalyptic number.

It is an amenable number.

1000101000001 is a deficient number, since it is larger than the sum of its proper divisors (1).

1000101000001 is an equidigital number, since it uses as much as digits as its factorization.

1000101000001 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 4.

Adding to 1000101000001 its reverse (1000001010001), we get a palindrome (2000102010002).

It can be divided in two parts, 100010 and 1000001, that added together give a palindrome (1100011).

The spelling of 1000101000001 in words is "one trillion, one hundred one million, one", and thus it is an aban number.