1031000013 has 6 divisors (see below), whose sum is σ = 1489222254. Its totient is φ = 687333336.

The previous prime is 1030999993. The next prime is 1031000023. The reversal of 1031000013 is 3100001301.

It can be written as a sum of positive squares in only one way, i.e., 847857924 + 183142089 = 29118^2 + 13533^2 .

It is not a de Polignac number, because 1031000013 - 2¹⁷ = 1030868941 is a prime.

It is a super-2 number, since 2×1031000013² = 2125922053612000338, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (9), and also a Moran number because the ratio is a prime number: 114555557 = 1031000013 / (1 + 0 + 3 + 1 + 0 + 0 + 0 + 0 + 1 + 3).

It is a junction number, because it is equal to n+sod(n) for n = 1030999959 and 1031000004.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (1031000023) by changing a digit.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 57277770 + ... + 57277787.

It is an arithmetic number, because the mean of its divisors is an integer number (248203709).

Almost surely, 2^1031000013 is an apocalyptic number.

It is an amenable number.

1031000013 is a deficient number, since it is larger than the sum of its proper divisors (458222241).

1031000013 is a wasteful number, since it uses less digits than its factorization.

1031000013 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 114555563 (or 114555560 counting only the distinct ones).

The product of its (nonzero) digits is 9, while the sum is 9.

The square root of 1031000013 is about 32109.1889184389. The cubic root of 1031000013 is about 1010.2283615909.

Adding to 1031000013 its reverse (3100001301), we get a palindrome (4131001314).

The spelling of 1031000013 in words is "one billion, thirty-one million, thirteen", and thus it is an aban number and an uban number.