10513 has 2 divisors, whose sum is σ = 10514.
Its totient is φ = 10512.
The previous prime is 10501. The next prime is 10529. The reversal of 10513 is 31501.
10513 = 722 + 732.
It is a weak prime.
It can be written as a sum of positive squares in only one way, i.e., 5329 + 5184 = 73^2 + 72^2
It is a cyclic number.
It is a de Polignac number, because none of the positive numbers 2k-10513 is a prime.
It is a super-2 number, since 2×105132 = 221046338, which contains 22 as substring.
It is a self number, because there is not a number n which added to its sum of digits gives 10513.
It is not a weakly prime, because it can be changed into another prime (10313) by changing a digit.
It is a pernicious number, because its binary representation contains a prime number (5) of ones.
It is a polite number, since it can be written as a sum of consecutive naturals, namely, 5256 + 5257.
It is an arithmetic number, because the mean of its divisors is an integer number (5257).
210513 is an apocalyptic number.
10513 is the 73-rd centered square number.
It is an amenable number.
10513 is a deficient number, since it is larger than the sum of its proper divisors (1).
10513 is an equidigital number, since it uses as much as digits as its factorization.
10513 is an odious number, because the sum of its binary digits is odd.
The product of its (nonzero) digits is 15, while the sum is 10.
The square root of 10513 is about 102.5329215423.
The cubic root of 10513 is about 21.9066290754.
The spelling of 10513 in words is "ten thousand, five hundred thirteen".