10001 has 4 divisors (see below), whose sum is σ = 10212. Its totient is φ = 9792.

The previous prime is 9973. The next prime is 10007.

10001 is nontrivially palindromic in base 10.

It is a Cunningham number, because it is equal to 10⁴+1.

It is a semiprime because it is the product of two primes.

It can be written as a sum of positive squares in 2 ways, for example, as 5776 + 4225 = 76^2 + 65^2 .

It is a sliding number, since 10001 = 1 + 10000 and 1/1 + 1/10000 = 1.0001.

It is a cyclic number.

It is a de Polignac number, because none of the positive numbers 2^k-10001 is a prime.

10001 is a strobogrammatic number because it is the same when read upside-down.

It is a deceptive number, since it divides R₁₀₀₀₀.

It is a Duffinian number.

It is a junction number, because it is equal to n+sod(n) for n = 9973 and 10000.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (10007) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 5 + ... + 141.

It is an arithmetic number, because the mean of its divisors is an integer number (2553).

2¹⁰⁰⁰¹ is an apocalyptic number.

It is an amenable number.

10001 is a deficient number, since it is larger than the sum of its proper divisors (211).

10001 is an equidigital number, since it uses as much as digits as its factorization.

10001 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 210.

The product of its (nonzero) digits is 1, while the sum is 2.

The square root of 10001 is about 100.0049998750. The cubic root of 10001 is about 21.5450650213.

It can be divided in two parts, 1000 and 1, that added together give a palindrome (1001).

The spelling of 10001 in words is "ten thousand, one", and thus it is an iban number.