12577 has 2 divisors, whose sum is σ = 12578. Its totient is φ = 12576.

The previous prime is 12569. The next prime is 12583. The reversal of 12577 is 77521.

It is a strong prime.

It can be written as a sum of positive squares in only one way, i.e., 12321 + 256 = 111^2 + 16^2 .

It is an emirp because it is prime and its reverse (77521) is a distict prime.

It is a cyclic number.

It is not a de Polignac number, because 12577 - 2³ = 12569 is a prime.

It is a plaindrome in base 10.

It is not a weakly prime, because it can be changed into another prime (12517) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 6288 + 6289.

It is an arithmetic number, because the mean of its divisors is an integer number (6289).

2¹²⁵⁷⁷ is an apocalyptic number.

It is an amenable number.

12577 is a deficient number, since it is larger than the sum of its proper divisors (1).

12577 is an equidigital number, since it uses as much as digits as its factorization.

12577 is an odious number, because the sum of its binary digits is odd.

The product of its digits is 490, while the sum is 22.

The square root of 12577 is about 112.1472246647. The cubic root of 12577 is about 23.2555002981.

It can be divided in two parts, 125 and 77, that added together give a palindrome (202).

The spelling of 12577 in words is "twelve thousand, five hundred seventy-seven".