137993 has 2 divisors, whose sum is σ = 137994. Its totient is φ = 137992.

The previous prime is 137983. The next prime is 137999. The reversal of 137993 is 399731.

It is a happy number.

137993 is nontrivially palindromic in base 11.

It is a strong prime.

It can be written as a sum of positive squares in only one way, i.e., 73984 + 64009 = 272^2 + 253^2 .

It is an emirp because it is prime and its reverse (399731) is a distict prime.

It is a cyclic number.

It is not a de Polignac number, because 137993 - 2⁸ = 137737 is a prime.

It is a Sophie Germain prime.

It is a Curzon number.

It is not a weakly prime, because it can be changed into another prime (137999) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 68996 + 68997.

It is an arithmetic number, because the mean of its divisors is an integer number (68997).

2¹³⁷⁹⁹³ is an apocalyptic number.

It is an amenable number.

137993 is a deficient number, since it is larger than the sum of its proper divisors (1).

137993 is an equidigital number, since it uses as much as digits as its factorization.

137993 is an odious number, because the sum of its binary digits is odd.

The product of its digits is 5103, while the sum is 32.

The square root of 137993 is about 371.4740906174. The cubic root of 137993 is about 51.6756187517.

The spelling of 137993 in words is "one hundred thirty-seven thousand, nine hundred ninety-three".