12961 has 4 divisors (see below), whose sum is σ = 13972. Its totient is φ = 11952.

The previous prime is 12959. The next prime is 12967. The reversal of 12961 is 16921.

12961 = T₃₈ + T₃₉ + ... + T₅₀.

12961 = 80² + 81².

12961 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

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 6561 + 6400 = 81^2 + 80^2 .

It is a cyclic number.

It is not a de Polignac number, because 12961 - 2¹ = 12959 is a prime.

It is an Ulam number.

It is an alternating number because its digits alternate between odd and even.

It is a Duffinian number.

12961 is a lucky number.

It is not an unprimeable number, because it can be changed into a prime (12967) 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, 486 + ... + 511.

It is an arithmetic number, because the mean of its divisors is an integer number (3493).

2¹²⁹⁶¹ is an apocalyptic number.

12961 is the 81-st centered square number.

It is an amenable number.

12961 is a deficient number, since it is larger than the sum of its proper divisors (1011).

12961 is an equidigital number, since it uses as much as digits as its factorization.

12961 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1010.

The product of its digits is 108, while the sum is 19.

The square root of 12961 is about 113.8463877336. The cubic root of 12961 is about 23.4898099777.

It can be divided in two parts, 129 and 61, that added together give a triangular number (190 = T₁₉).

The spelling of 12961 in words is "twelve thousand, nine hundred sixty-one".