72577 has 2 divisors, whose sum is σ = 72578. Its totient is φ = 72576.

The previous prime is 72559. The next prime is 72613. The reversal of 72577 is 77527.

It is a happy number.

It is a weak prime.

It can be written as a sum of positive squares in only one way, i.e., 46656 + 25921 = 216^2 + 161^2 .

It is an emirp because it is prime and its reverse (77527) is a distict prime.

It is a cyclic number.

It is not a de Polignac number, because 72577 - 2¹¹ = 70529 is a prime.

72577 is a lucky number.

It is a congruent number.

It is not a weakly prime, because it can be changed into another prime (72547) 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, 36288 + 36289.

It is an arithmetic number, because the mean of its divisors is an integer number (36289).

2⁷²⁵⁷⁷ is an apocalyptic number.

It is an amenable number.

72577 is a deficient number, since it is larger than the sum of its proper divisors (1).

72577 is an equidigital number, since it uses as much as digits as its factorization.

72577 is an odious number, because the sum of its binary digits is odd.

The product of its digits is 3430, while the sum is 28.

The square root of 72577 is about 269.4011878222. The cubic root of 72577 is about 41.7125113177.

Subtracting 72577 from its reverse (77527), we obtain a triangular number (4950 = T₉₉).

The spelling of 72577 in words is "seventy-two thousand, five hundred seventy-seven".