688013 has 2 divisors, whose sum is σ = 688014. Its totient is φ = 688012.

The previous prime is 688003. The next prime is 688027. The reversal of 688013 is 310886.

It is a weak prime.

It can be written as a sum of positive squares in only one way, i.e., 619369 + 68644 = 787^2 + 262^2 .

It is a cyclic number.

It is not a de Polignac number, because 688013 - 2⁶ = 687949 is a prime.

It is equal to p₅₅₆₆₄ and since 688013 and 55664 have the same sum of digits, it is a Honaker prime.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 688013.

It is not a weakly prime, because it can be changed into another prime (688003) 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, 344006 + 344007.

It is an arithmetic number, because the mean of its divisors is an integer number (344007).

2⁶⁸⁸⁰¹³ is an apocalyptic number.

It is an amenable number.

688013 is a deficient number, since it is larger than the sum of its proper divisors (1).

688013 is an equidigital number, since it uses as much as digits as its factorization.

688013 is an odious number, because the sum of its binary digits is odd.

The product of its (nonzero) digits is 1152, while the sum is 26.

The square root of 688013 is about 829.4654905420. The cubic root of 688013 is about 88.2806552731.

Adding to 688013 its reverse (310886), we get a palindrome (998899).

It can be divided in two parts, 68801 and 3, that multiplied together give a triangular number (206403 = T₆₄₂).

The spelling of 688013 in words is "six hundred eighty-eight thousand, thirteen".