2013123131137 has 2 divisors, whose sum is σ = 2013123131138. Its totient is φ = 2013123131136.

The previous prime is 2013123131113. The next prime is 2013123131147. The reversal of 2013123131137 is 7311313213102.

It is a strong prime.

It can be written as a sum of positive squares in only one way, i.e., 1459109380096 + 554013751041 = 1207936^2 + 744321^2 .

It is a cyclic number.

It is not a de Polignac number, because 2013123131137 - 2³⁵ = 1978763392769 is a prime.

It is a super-2 number, since 2×2013123131137² (a number of 25 digits) contains 22 as substring.

It is not a weakly prime, because it can be changed into another prime (2013123131147) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (23) of ones.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 1006561565568 + 1006561565569.

It is an arithmetic number, because the mean of its divisors is an integer number (1006561565569).

Almost surely, 2^{2013123131137} is an apocalyptic number.

It is an amenable number.

2013123131137 is a deficient number, since it is larger than the sum of its proper divisors (1).

2013123131137 is an equidigital number, since it uses as much as digits as its factorization.

2013123131137 is an odious number, because the sum of its binary digits is odd.

The product of its (nonzero) digits is 2268, while the sum is 28.

Adding to 2013123131137 its reverse (7311313213102), we get a palindrome (9324436344239).

The spelling of 2013123131137 in words is "two trillion, thirteen billion, one hundred twenty-three million, one hundred thirty-one thousand, one hundred thirty-seven".