37813 has 2 divisors, whose sum is σ = 37814. Its totient is φ = 37812.

The previous prime is 37811. The next prime is 37831. The reversal of 37813 is 31873.

37813 = 137² + 138².

Together with next prime (37831) it forms an Ormiston pair, because they use the same digits, order apart.

It is a weak prime.

It can be written as a sum of positive squares in only one way, i.e., 19044 + 18769 = 138^2 + 137^2 .

It is an emirp because it is prime and its reverse (31873) is a distict prime.

It is a cyclic number.

It is not a de Polignac number, because 37813 - 2¹ = 37811 is a prime.

Together with 37811, it forms a pair of twin primes.

37813 is a lucky number.

It is a congruent number.

It is not a weakly prime, because it can be changed into another prime (37811) by changing a digit.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 18906 + 18907.

It is an arithmetic number, because the mean of its divisors is an integer number (18907).

2³⁷⁸¹³ is an apocalyptic number.

37813 is the 138-th centered square number.

It is an amenable number.

37813 is a deficient number, since it is larger than the sum of its proper divisors (1).

37813 is an equidigital number, since it uses as much as digits as its factorization.

37813 is an odious number, because the sum of its binary digits is odd.

The product of its digits is 504, while the sum is 22.

The square root of 37813 is about 194.4556504707. The cubic root of 37813 is about 33.5645151644.

The spelling of 37813 in words is "thirty-seven thousand, eight hundred thirteen".