1010000001001 has 2 divisors, whose sum is σ = 1010000001002. Its totient is φ = 1010000001000.

The previous prime is 1010000000959. The next prime is 1010000001071. The reversal of 1010000001001 is 1001000000101.

It is a weak prime.

It can be written as a sum of positive squares in only one way, i.e., 543751386025 + 466248614976 = 737395^2 + 682824^2 .

It is a cyclic number.

It is not a de Polignac number, because 1010000001001 - 2⁹ = 1010000000489 is a prime.

It is not a weakly prime, because it can be changed into another prime (1010000001071) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (23) of ones.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 505000000500 + 505000000501.

It is an arithmetic number, because the mean of its divisors is an integer number (505000000501).

Almost surely, 2^{1010000001001} is an apocalyptic number.

It is an amenable number.

1010000001001 is a deficient number, since it is larger than the sum of its proper divisors (1).

1010000001001 is an equidigital number, since it uses as much as digits as its factorization.

1010000001001 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 1010000001001 its reverse (1001000000101), we get a palindrome (2011000001102).

It can be divided in two parts, 101000000100 and 1, that added together give a palindrome (101000000101).

The spelling of 1010000001001 in words is "one trillion, ten billion, one thousand, one".