7993 has 2 divisors, whose sum is σ = 7994. Its totient is φ = 7992.

The previous prime is 7963. The next prime is 8009. The reversal of 7993 is 3997.

7993 is nontrivially palindromic in base 8.

7993 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is the 37-th star number.

It is a strong prime.

It can be written as a sum of positive squares in only one way, i.e., 5184 + 2809 = 72^2 + 53^2 .

It is a cyclic number.

It is not a de Polignac number, because 7993 - 2^{9} = 7481 is a prime.

It is a plaindrome in base 15.

It is not a weakly prime, because it can be changed into another prime (7933) by changing a digit.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 3996 + 3997.

It is an arithmetic number, because the mean of its divisors is an integer number (3997).

2^{7993} is an apocalyptic number.

It is an amenable number.

7993 is a deficient number, since it is larger than the sum of its proper divisors (1).

7993 is an equidigital number, since it uses as much as digits as its factorization.

7993 is an odious number, because the sum of its binary digits is odd.

The product of its digits is 1701, while the sum is 28.

The square root of 7993 is about 89.4035793467. The cubic root of 7993 is about 19.9941649645.

Multiplying 7993 by its reverse (3997), we get a triangular number (31948021 = T_{7993}).

It can be divided in two parts, 7 and 993, that added together give a cube (1000 = 10^{3}).

The spelling of 7993 in words is "seven thousand, nine hundred ninety-three".

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