513312013 has 2 divisors, whose sum is σ = 513312014. Its totient is φ = 513312012.

The previous prime is 513311969. The next prime is 513312017. The reversal of 513312013 is 310213315.

It is a strong prime.

It can be written as a sum of positive squares in only one way, i.e., 476854569 + 36457444 = 21837^2 + 6038^2 .

It is a cyclic number.

It is not a de Polignac number, because 513312013 - 2⁹ = 513311501 is a prime.

It is a super-2 number, since 2×513312013² = 526978445380224338, which contains 22 as substring.

It is a congruent number.

It is not a weakly prime, because it can be changed into another prime (513312017) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 256656006 + 256656007.

It is an arithmetic number, because the mean of its divisors is an integer number (256656007).

Almost surely, 2^513312013 is an apocalyptic number.

It is an amenable number.

513312013 is a deficient number, since it is larger than the sum of its proper divisors (1).

513312013 is an equidigital number, since it uses as much as digits as its factorization.

513312013 is an odious number, because the sum of its binary digits is odd.

The product of its (nonzero) digits is 270, while the sum is 19.

The square root of 513312013 is about 22656.3901140495. The cubic root of 513312013 is about 800.6827572416.

Adding to 513312013 its reverse (310213315), we get a palindrome (823525328).

The spelling of 513312013 in words is "five hundred thirteen million, three hundred twelve thousand, thirteen".